5

Which one can be a solution for the following differential equation?y' +4y +13y =e-% cos(3x) + 18e 2x4) Axe 2* cos(3x) + Bxe 2X sin(3x) + Cxe-ex b)y = Ae-ex co...

Question

Which one can be a solution for the following differential equation?y' +4y +13y =e-% cos(3x) + 18e 2x4) Axe 2* cos(3x) + Bxe 2X sin(3x) + Cxe-ex b)y = Ae-ex cos(3x) + Be c)y = Zxe 2x (Acos(3x) + Bsin(3x)) + 2e 21 d)y = e "*C (Acos(3x) + Bsin(3x)) + Cxe 2 e)y Xe (Acos(3x) + Bsin(3x)) + 2e

Which one can be a solution for the following differential equation? y' +4y +13y =e-% cos(3x) + 18e 2x 4) Axe 2* cos(3x) + Bxe 2X sin(3x) + Cxe-ex b)y = Ae-ex cos(3x) + Be c)y = Zxe 2x (Acos(3x) + Bsin(3x)) + 2e 21 d)y = e "*C (Acos(3x) + Bsin(3x)) + Cxe 2 e)y Xe (Acos(3x) + Bsin(3x)) + 2e



Answers

The solution of the differential equation $\left(x \cos x-\sin x+y x^{2}\right) d x+x^{3} d y=0$ is equal to (A) $\frac{\sin x}{x}+x y=c$ (B) $\frac{\sin x}{x}+x=c$ (C) $\frac{\sin x}{x}+y=c$ (D) None of these

Here I group these two tops and also divide all the terms of this equation by x squared. So when I do that I get X. Cossacks minus of cynics over x squared times of dx plus. The term is X cubed. The way. When you divide by X grade we get xd way and this term is why X squared dx. So you do it by X squared you get y dx equals zero. No I can relate this uh this quantity. Yes. Did we do off sign X by X plus I can write this again. Group as the distribute two of x Y. And now I read the zero on the right side as a tribute to all some constant. So let's integrate hall the terms so we integrate like this. Remember that when you integrate the deputy of some function you just get only the function inside the derivative part. So here I'm going to get sign X by X plus uh integration of devotee of X, Y. I get x Y equals integration of divinity of constant. I simply get X. I'm sorry see so this is the solution to the required the differential question which means the option is correct

We will not solve this given differential equation that is to buy cynics DVD X equals two Cynics Cossacks minus Y squared cossacks Which satisfies this condition. Way of favour to equal to one. So for this I'm going to relate this differential commission and inform that we can integrate it. So let me write this as two Y cynics. The way by dicks, I bring this a negative Y squared cossacks to the website which means I will have press Y squared Cossacks. The call to. I can relate this to cynics as sign blocks using the standard techno metric identity. Now if you can observe these two terms basically is the differentiation of Y squared Cossacks. Sorry Y squared cynics. We can easily verify this. Suppose if you differentiate this Y squared Synnex will be getting y squared times differentiation of sin access Cossacks. Then I keep the cynics as it is multiply with the product of y squared differentiation. Always card, which is a two way. Do you worry about the X. So basically I have these two terms as I have it here which means I can replace these two terms as just a differentiation of y squared cynics which I I don't hear. And on the right side we still have this sign towards now we can integrate board sets. So we put this integration with respect to be X. So we have the formula integration of the beauty of a for fax is basically a vortex which means here I will get why is quite cynics there is equal to integration of science to access negative cost works by two. And then we put this integration Constancy. Now we basically got the solution without playing the initial conditions. Let's apply the initial condition that is X equals fiber to and Y equal to one. So we have to substitute the value of X equal to paper too. Why I called the one into the situation and when we do that uh why is quite basically that is one squared is one and sign off excess private to sign fiber to is one. So this is equal to have negative one way to Times of course off two times of Can do it here cause of two terms of replace exploit private too, which means this is cause of the cause of 80 and 81. Then we have this seat So therefore this side we have one and this is 1900 2 times 91 is one way to plus C. This means I can find the value is equal to one minus one byte, which is one way to. So the value of C equal to one by two. We can substitute into the solution equation. So let me do that. We can over here. This is on by two. We just clean this up for some space. Which Okay, so now we can multiply both sides by two. They will be getting two. Y squared cynics is equal to 1- costs two weeks. Okay, so this is now we can instead techno metric guarantee one minus cost to excess basically to science codex. So decide how to square Cynics can cancel these two truths like this. Then I get y squared cynics or if I divide both sides by cynics, I'll be getting y squared equal to sign X. So this is in tractor solution after given differential equation, which means the correct answer for this question is option in.

We need to determine the solution of this given differential equation to find the solution. I'm going to read it in a form that we could easily integrated. So let me consider these terms as a group that is three X Y squared dy plus Y Q bx as a group. So let me write on this we have three xy squared dy plus Y que dx this I can stir as a group and then I write down the remaining terms that is X. Times of sine of X. Y. Dy plus why times of sign off X Y D. D. S. So that we have the common factor sign off X. Y from both these terms which means I can factor the sine of X. Y and then I'll be lived with the X. Dy plus uh I D x equal to zero. Now I can write down these two terms as just a day away to off X Y Q. You can easily verify that we should differentiate exploit, you will be getting these two terms and similarly I can write on these terms Sin exploit. I read on as it is can write on these two terms as a delegate to offer x Y. He called to zero. Now integrate H terms uh as far as the right side so do this integration symbol and when I integrate the delivery to of some function will basically get that function. So integration of differentiation of X Y cube is basically X Y Q plus to integrate this one. We can conserve this formula Sin x dx integration of sin x dx is basically negative cossacks. So it is in the similar form except that we have signed off X. Y. And the Y. Two of X. Y. So basically when you integrate this we'll be getting negative because of X. Y. Yeah. And when you integrate zero we'll get constancy. So this is the required a differential equation, which means the option A. Is correct.

In the problem we have been given do to Y. Upon the excess choir minus to develop on duty Plus why that equals two two x plus x square less sign to the X. Now here this can be too nice day Squire minus two D Plus one that equals zero. Or it is um Squire minus story um plus one that equals zero So M -100 sq becomes zero. Therefore M equals one and one. These are reported roots. So we have complimentary solution becomes seven plus Say two x into each barracks further to find the particular solution. So particular solution will be A plus B. X plus C. X. Squire plus E. Into science three X plus F cost three X. Therefore day of why sorry this is Y. P. So operator days apply to wipe therefore it becomes B plus to see X plus T. E cost three X minus three F. Scientifics. Now it is the Squire wipe that is equal to two C -9 A. Scientifics minus nine F. Austria X. Now we have to apply it and this vacation therefore this become mhm. Two C minus nine E. Signed three X minus nine F. Cost three x minus to b -4 C. X minus six. A cost three X plus six F. Scientifics plus eight plus M. B. X. Plus C. X. Squire plus E. Signed to the X plus F. Cost three X. That equals two two x plus x. Squire plus Scientifics. Now we have to compare the coffee since and get the villas off A. B. C. D. And further variables. Therefore we have two C- to B Plus A. That equals to zero. And further this is the question one. Now we have further equation that is minus nine E. Plus six f. plus e. That equals one. This is like an aggression -4 C Plus B. That equals to this is the third equation C equals one minus nine F minus 60 Plus F. That it was zero, This is 4th aggression minus eight F. This become, now the other occupation is six f minus 80 that equals one. This is 50 questions. Now here mhm. From this point we have the value of see here, so this become Value of B will be six, See is one, B. Is six. Therefore we have the value of A. That is equal to 10. Now we have the values of abc. So here we don't have the value of the N. F. Therefore we have the equation that is minus eight F. So from ford we have minus a death -6 E. That it was zero and equation five This is six F -80 that equals one. So this is a question five. Now women reply these equations with three and four. Therefore this becomes mhm -24 F -18 e. That equals zero And it's 24 f minor studied to E. That equals for and adding these two equations. Therefore it is cancels each other. Here is 50 e. That equals four. Therefore he is equal to -2 upon 25 and we have F. Is equal to three upon 50. So further we have the overall solution the solution become why is equal to Y. C plus white B. Further this is seven Plus c. two. Here is X. So this is X. And to eat the barracks plus 10 plus six x plus x squared -2 upon 25 signed today. X Plus three upon 50 Cost three X. So this is our equation and this is the answer.


Similar Solved Questions

5 answers
Solve UrE Inltial value Proticm: '21M points) Use separation = 'variables cscy,Y(1) "213) (15 pcinis) In 2012 Ine Ojy Eastvalc_cocialco50000 0ssumng Grotth rie direchiy Rrcporliona Jopulato ? given tino fInd Ate ear [e Popllation wil doublo # tho pepulation was 75CD0 [ 2017 .
solve UrE Inltial value Proticm: '21M points) Use separation = 'variables cscy,Y(1) "2 13) (15 pcinis) In 2012 Ine Ojy Eastvalc_ cocialco 50000 0ssumng Grotth rie direchiy Rrcporliona Jopulato ? given tino fInd Ate ear [e Popllation wil doublo # tho pepulation was 75CD0 [ 2017 ....
5 answers
PLEASEREADThis is for my physics class and [ need help understanding how to do the problem below so that I can do others like it on my ownPlease include explanations_Thank you in advancel
PLEASEREAD This is for my physics class and [ need help understanding how to do the problem below so that I can do others like it on my own Please include explanations_ Thank you in advancel...
5 answers
14901225 OpenitFenetaDeJule GLEMae^1 alilFchaHane{Ass Onmeni ? ChapterThe Genctic CodeMaathu codo; lorleandmtet Do MAcotkJmng En Uannd enj 0luurona ol the Iree ~cp codon (UWA UNG, ad UGAAPjnt @ Tarkaben ol (JRHAQuina CodnenudeolEitirdneed Rhoniain Ir Dec4o JminAenJun-o Ioloamqnrt Ialule ATGGCAAGALL Lanco ocddt uting loehynhena mSLpue5ut-Tt Lyt-GhlAyallabla Hilnuel0; CNcCattinn] aMinj 3 REToconucogo
14901225 Openit Feneta DeJule GLEMae^1 alilFcha Hane {Ass Onmeni ? Chapter The Genctic Code Maat hu codo; lor leand mtet Do MAcotkJmng En Uannd enj 0luur ona ol the Iree ~cp codon (UWA UNG, ad UGAA Pjnt @ Tarkaben ol (JRHA Quina Codne nudeol Eitirdneed Rhoniain Ir Dec4o JminAenJun-o Ioloamqnrt Ialul...
5 answers
The demand curve for product is given by q = 1000 Sp wherep is the price. Find the price that maximizes revenue for sales of this product:Round your answer to two decimal places:To maximize revenue; the price of the product should be $
The demand curve for product is given by q = 1000 Sp wherep is the price. Find the price that maximizes revenue for sales of this product: Round your answer to two decimal places: To maximize revenue; the price of the product should be $...
5 answers
D: May 9 at 929pm iz InstructionsQuestion 125 ptsUse the Root Test to determine the convergence or divergence of the series2/z| J02_divergesRoot Test inconclusiveconvergesPreviousNext
d: May 9 at 929pm iz Instructions Question 12 5 pts Use the Root Test to determine the convergence or divergence of the series 2/z| J02_ diverges Root Test inconclusive converges Previous Next...
5 answers
Question 7 (1 point)Which one is a strong reducing agent?OA NAD of the NAD -NADH coupleB) 02 of thc 02-HzO coupleC) HzO of the 02-HzO coupleD) NADH of the NAD NADH coupleQuestion 8 (1 point) The proton binding residuc in the subunit of ATP synthasc isOA) cytochrome €B) aspartic acidcopperD) ATPE} F1 particle
Question 7 (1 point) Which one is a strong reducing agent? OA NAD of the NAD -NADH couple B) 02 of thc 02-HzO couple C) HzO of the 02-HzO couple D) NADH of the NAD NADH couple Question 8 (1 point) The proton binding residuc in the subunit of ATP synthasc is OA) cytochrome € B) aspartic acid co...
5 answers
Humulene and $alpha$ -caryophyllene alcohol are terpene constituents of camation extracts. The former is converted into the latter by acid-catalyzed hydration in one step. Write a mechanism. (Hint: Follow the labeled carbon atoms retrosynthetically. The mechanism includes carbocation-induced cyclizations and hydrogen and alkyl-group migrations.)
Humulene and $alpha$ -caryophyllene alcohol are terpene constituents of camation extracts. The former is converted into the latter by acid-catalyzed hydration in one step. Write a mechanism. (Hint: Follow the labeled carbon atoms retrosynthetically. The mechanism includes carbocation-induced cycliza...
5 answers
Show that the Frenet-Serret basis rotates as a solid body with rotation vector per unit of curve length, $oldsymbol{Omega}=kappa oldsymbol{b}+au oldsymbol{t}$.
Show that the Frenet-Serret basis rotates as a solid body with rotation vector per unit of curve length, $oldsymbol{Omega}=kappa oldsymbol{b}+ au oldsymbol{t}$....
5 answers
Use Norton's Theorem to calculate the current through 702 resistor; 4 Marks100407024220120 V
Use Norton's Theorem to calculate the current through 702 resistor; 4 Marks 100 40 70 242 20 120 V...
5 answers
43. What is the known function of SNARE proteins?Form transport -vosictes Mediate fusion of transport vesicles with target membranes Control the initial trafficking and docking of transport vesicles target membranes Ensure that onlly properly folded proteins are packaged into transport vesicles Mediate vesicle attachment to actin filaments
43. What is the known function of SNARE proteins? Form transport -vosictes Mediate fusion of transport vesicles with target membranes Control the initial trafficking and docking of transport vesicles target membranes Ensure that onlly properly folded proteins are packaged into transport vesicles Med...
5 answers
Fill in the first blank in each centenca below with overestimates Or underestimates and the second blank with increasing: decreasing; concave up_ concave down_On the interval [a. 6], Rz $ arebecauseon |a,b .On the interval |a.6, Ln arebecauseOn the interval |a.b;, Mn arebecauseOn the interval [b,c. Rn arebecauseb,c].On the interval [b,c]. Ln` arebecauseon (6,c].On the interval [b,c . Mnbecauseon (6,c].
Fill in the first blank in each centenca below with overestimates Or underestimates and the second blank with increasing: decreasing; concave up_ concave down_ On the interval [a. 6], Rz $ are because on |a,b . On the interval |a.6, Ln are because On the interval |a.b;, Mn are because On the interva...
5 answers
A small mass charged sphere ( q= 3 AC ) is attached by an insulating string to the surface Of a very large conductor with a surface charge density of & = 49.8 /LC. Given that the string makes an angle with the surface equal t0 30 degrees; find the tension ( in N)in the string use €0 8.8542*10-12 EmSelect one 0A. 66.67OB. 16.87 OC. 33.75 OD. 19.48OE. 50.62ENGString
A small mass charged sphere ( q= 3 AC ) is attached by an insulating string to the surface Of a very large conductor with a surface charge density of & = 49.8 /LC. Given that the string makes an angle with the surface equal t0 30 degrees; find the tension ( in N)in the string use €0 8.8542...
5 answers
What helps to stabilize the secondary structures and the overall3º fold of a protein.
What helps to stabilize the secondary structures and the overall 3º fold of a protein....
5 answers
Formula for the tellurite ion:
formula for the tellurite ion:...
3 answers
Suppose survey of adults and teens ages 12-17) in certain country was conducted to determine the number of texts sent Number of Texts Adults eens single day - one Construct relative frequency distribution for adults. Construct relative frequency distribution for teens Construct side-by-side relative frequency bar graph: Compare the texting habits of adults and teens 100 100None 1-10 11-20 21-50 51-100100 (Round to three decimal places as needed_
Suppose survey of adults and teens ages 12-17) in certain country was conducted to determine the number of texts sent Number of Texts Adults eens single day - one Construct relative frequency distribution for adults. Construct relative frequency distribution for teens Construct side-by-side relative...
4 answers
Browning nterchemical property describes the tendency of a ChemicaLvs Physical Eropetties (Recall that . property describes the tendency of @ chemitol 'chonge_ physical {uostonce undergo 'physical quality of the substance) phlitol chunol describes suostarce underc Label each of thc following chemica physical propertyFlammabilitycorrosiycncs;Sour tasteDensityBoiling point
Browning nter chemical property describes the tendency of a ChemicaLvs Physical Eropetties (Recall that . property describes the tendency of @ chemitol 'chonge_ physical {uostonce undergo 'physical quality of the substance) phlitol chunol describes suostarce underc Label each of thc follow...
5 answers
Question 7Below are tWO Integration problems along' wich student'$ answers t0 themEvaluate the Indefinite IntegraldxStudents answver:+4V7) + € 2x2 Identify two mistakes In tne answer and FInd the Integral; Evaluate the Indeiinite Integra csc?(x?) dxSiudenis answer=sec (4*4)ldentifyto mistakesIn (ne ansier ano Tino the integraT T T € Parpraph 0o D 0 6AftalJ(12puType nee I0 *€4'4n
Question 7 Below are tWO Integration problems along' wich student'$ answers t0 them Evaluate the Indefinite Integral dx Students answver: +4V7) + € 2x2 Identify two mistakes In tne answer and FInd the Integral; Evaluate the Indeiinite Integra csc?(x?) dx Siudenis answer= sec (4*4) ld...
5 answers
Acoudictng thiltod oflength L is suspended by two flexible wies Bhown nthe figure: The rodhhas 1ass per ut lengtn 0.024 kglm Wkat . JWTri C3SN[lh drough the rod for the tension in the supporting flexible wires to be zero if the maguetic field is B 220 Tesla? What 1s the required drrection for the ctner? (eAL, 9Buds)BinA 120 mAto the rightB.50 mA to the rightC. 107 mA to the rightD. 98 mA to the leftReset Selection
Acoudictng thiltod oflength L is suspended by two flexible wies Bhown nthe figure: The rodhhas 1ass per ut lengtn 0.024 kglm Wkat . JWTri C3SN[lh drough the rod for the tension in the supporting flexible wires to be zero if the maguetic field is B 220 Tesla? What 1s the required drrection for the c...
5 answers
Lc f.0) = Jstdl Fuluk fl2 ,2), q X- Jre 's domam anA mn2 bet $l.9) = xb2xt-& =k, K:bz 0, skolch d Iwt Curve s of flx)-k, fv Kel) 2, D.
Lc f.0) = Jstdl Fuluk fl2 ,2), q X- Jre 's domam anA mn 2 bet $l.9) = xb2xt-& =k, K:bz 0, skolch d Iwt Curve s of flx)-k, fv Kel) 2, D....
5 answers
Aehelri 20700 X -roi d, jWto ,42= 07 &W : =4
Aehelri 20700 X -roi d, jWto ,42= 07 &W : =4...

-- 0.022760--