5

Solve the given initial value problem.y'' + 4y' + 4y =0, y(−1)= 3, y'(−1)= 2y(t)?...

Question

Solve the given initial value problem.y'' + 4y' + 4y =0, y(−1)= 3, y'(−1)= 2y(t)?

Solve the given initial value problem. y'' + 4y' + 4y = 0, y(−1) = 3, y'(−1) = 2 y(t)?



Answers

Solve the initial value problem. $$y^{\prime \prime}+4 y=0, y(0)=2, y^{\prime}(0)=-3$$

Yeah, we want to solve the a separation of variables. The initial value problem given by the differential equation, Y prime equals two minus Y. And the initial conditions live zero equals three. There are three necessary steps we followed to complete this problem first we'll isolate our variables on either side of the equation. So put all white terms, left all extras in right way. Then we'll integrate both sides of the equation and solve the resultant in terms of Y. So we want why some function of X. Since step two has an indefinite integral where we will be left with a constant integration, C or a. So in step three we use the initial conditions to solve for C. Or a and finish the problem. So why prime is dy dx? We can first right do 1/2 minus Y equals D X, integrating both sides, gifts negative Ln of two minus Y equals x plus E. The constant integration solving gives Y equals negative A either negative exposed to where we've taken E to the sea and turned it into A. So now we can solve for C. Using initial value Y zero equals +33 equals negative +80 plus two, or A equals negative one. This gives Y equals E. To the negative X plus two.

Hello, everyone. In this given version, we have toe solve the initial value problem. The question is why devilish minus six Swedish plus 10 by it's a question and to initial conditions are given. That is wise. You guys too. And why does judo is three right? So first real light oxidant equation. So you get ice with minus six hour plus tenets Request ejido on the routes off. These equations are six plus minus and the 36 minus 40 divided by toe which comes out Toby six Celtics comes out to be three plus minus iota. So these are the 32 off the Given the question, since the roots are imaginary roots. So we have the general solution that is to the body X See one Cosby X plus C to sign bx tonight. Now, uh, a question. This is given the book so we'll plug the values from the roots that is is request to three and basic was too one like so it took about three x see, even cortex plus C to cynics. Now we have to find the values of C one and C two to find the value of C one and C two, We have toe put initial conditions. So why did you go? Is equal to which is equals to U to the power ejido. See you on cost you plus C to sign Jill. So this will give the u. N. Has to like now we will differentiate it. So when we differentiate the VX, we get virus access I hated about three x minus even cynics plus C two Cossacks plus three to the Power three x See you on Cossacks, Stephen cause t a X. So this even cause three X plus Ito Synnex. Right now we have the second initial value problem. That is why the studio is equal to three. So we get to the college. Edo Um minus even signed judo plus C to cost, you know, plus three to depart Judo C one cause street off Aceto Sandretto Like eso, this will result in, say, two plus 37 We know the value off Stephen. That s e questo. So c two plus, So this will give the result off Saito a spine astri Wright. Now we can put substitute the values off C one and C two in the general form. So we get wires created about three X to Cossacks minus three. Cynics. Right. So the sisters solution for the initial value problem.

In this problem we have in the shell Fellow Differential Equation, which is given by white double prime last three y, is equal to zero. Why zero is a call to one on twice prime cedar. It's according to three. Now we can sec it so this to function in creation, a psychiatrist to decommission, which is given by a T Square plus threes. A call to Syria This in place two years ago. Two. Squared off three I with Plus Linus No, let's recall the Pura when we have the complex route off the guy sophistication. They know we know the solutions. The General Solutions can be reaching us e to depart al flicks now, unfortunately, in this case al physical to zero because there is no real part. So this is going to be one time. See one time school sine squared off three x plus c. Two. I'm sign off. Squire rode off three x So this is going to be our general solution. So let's right tone the Purim. If Alfa Plus minus I beata are the solutions off, take actress sticky creation than the solutions competitiveness. So why is the country to the poor? Al fix times C. One time school sign beat X plus C two times Sign off be dykes. So there's that urine we are using in this problem. So now we have Why zero is they called to one? And why Prime Seaver? Is he going to three? So let's go back. If I use the condition why zero is equal to one. So we see that this time goes away and call Sign zero. It's simply is a call to one. So this implies C one is equal to one. So let's stick the derivative off. This life we have like prime mix is going to be C one times the derivative off course sign. It's a negative sign. Squire rode off three x Times Square Load off three plus C two times the derivative off court sign Ixis simply co sign Squire rode off three ex, followed by Sky Road off three So now we have the condition that why prime zero? Is it going to three? So this in place, If I take exit sickle to zero in this situation, then I end up getting C two time squared off. Two years ago, the three the same place he, too is called the square root of three. So then the political a solution can breed in us. Why is he going to co sign Squared off? Three x plus squared off? Three Signed off. Skye wrote off three x. So that's the specific solution afford initial.

Calling a bond second under a different question. A y double prime plus B y Prime Leslie. Why equal to zero? Then we can define the characteristic question I ask where plus b r plus c equal to zero. Now suppose that we have to distinguish route are one different from the aren't you? And then we have the generation why we go to the constancy one each of the ah one x plus The constancy to each are two x on in this question were given the Audi A wide about prime plus why prime minus y equal to zero with the initial value and the white prime on the zero you go to Trias Well, and now the first time we need to find characteristic equation will be to our square plus, uh, minus one equal to zero. And then, for this one, we can use the quadratic formula together. Want to it? We go to minus one plus Amanda Square root under one Manus, for I see where equals J plus, uh, eight. And then defended by far. Then we get into Q minus one. Bless semanas Ah, three divided by far. Don't get Nico too. It would use the plus began the manners Ah, half. And when used Ah, we got a half another minus. So we will be beautiful and we use a minus. You get to go to minus one here and therefore we have the general solution. It will be why, ego to Constance. Constancy one times each of the power. Ah, half X plus a constant CTO each of the power Manus X. And now if we try to look in the initial value here wiser, are we equal with you? Let's see one plus e to equals you three. Now it would use the what if we compute the distributive again? The white primary called You see one on with you each and about a half X minus C to each about minus x. From here we block in the initial initial value. We get equal with you the C one out with U minus t to equal to three from here and we need to solve the system in question. Now notice that you go over the line and we'll add them up. Then we get equal to the three c one hour to this one's gonna be There are here and then ik 026 Therefore, we have to see one ico to the ah, try a lower three cause you far And it means standard seat you It will equal with you the three minus e once three minus four to minus one. So it means that we have the final answer. Why Equal thio see one equal to far each and a half x c two equal to minus one each of about minus x


Similar Solved Questions

5 answers
A lamina is bounded by the curve r = 2cos 30 when <0 < & Assuming cOnstant density: 0 = k give the Lctungulur coordinates Of the centroid (5 Points).
A lamina is bounded by the curve r = 2cos 30 when <0 < & Assuming cOnstant density: 0 = k give the Lctungulur coordinates Of the centroid (5 Points)....
5 answers
Determine whether the following statement is true or false.{xlx is a whole number less than 3} = {0,1,2}
Determine whether the following statement is true or false. {xlx is a whole number less than 3} = {0,1,2}...
5 answers
Please match the fcllowing !H NMR spectrum with thc uppropriate compcundConpound:Selectzd CAgNee
Please match the fcllowing !H NMR spectrum with thc uppropriate compcund Conpound: Selectzd CAgNee...
5 answers
Given the values: n = 10, 5.5, =7, Sxy = -60, and Sxx = 20, what are the values of the least squares estimates for Bo and B1? bob1
Given the values: n = 10, 5.5, =7, Sxy = -60, and Sxx = 20, what are the values of the least squares estimates for Bo and B1? bo b1...
4 answers
ICB = P-!APT, and P is nonsingular, then det(B) = det (4) 00Let A be an k * k ltix in which each entry is 1. then det(klk - 4) = 0
ICB = P-!APT, and P is nonsingular, then det(B) = det (4) 0 0 Let A be an k * k ltix in which each entry is 1. then det(klk - 4) = 0...
1 answers
A net external force is applied to a $6.00-\mathrm{kg}$ object that is initially at rest. The net force component along the displacement of the object varies with the magnitude of the displacement as shown in the drawing. What is the speed of the object at $s=20.0 \mathrm{~m}$ ?
A net external force is applied to a $6.00-\mathrm{kg}$ object that is initially at rest. The net force component along the displacement of the object varies with the magnitude of the displacement as shown in the drawing. What is the speed of the object at $s=20.0 \mathrm{~m}$ ?...
5 answers
QuestionSolve the following initial-value problem.csc? (2) , V3 f' (c) = f(3) --3 3Provide your answer below:f(x)
Question Solve the following initial-value problem. csc? (2) , V3 f' (c) = f(3) --3 3 Provide your answer below: f(x)...
5 answers
In the reaction conrcinate diagram scen Belon Ucnrepresentativeenergythe rate determining stcp?bE6 DEAE?AE6AEA-AEIAE3AE?-AE]AEAAEL
In the reaction conrcinate diagram scen Belon Ucn representative energy the rate determining stcp? bE6 DE AE? AE6 AEA-AEI AE3 AE?-AE] AEA AEL...
5 answers
1- Which one of the following thermodynamic quantities is NOT astate function? (a) Gibbs free energy (b) Enthalpy (c) Entropy (d)Internal energy (e) WorkREAD MORE
1- Which one of the following thermodynamic quantities is NOT a state function? (a) Gibbs free energy (b) Enthalpy (c) Entropy (d) Internal energy (e) WorkREAD MORE...
1 answers
Aspirin has the structural formula At body temperature $\left(37^{\circ} \mathrm{C}\right), K_{a}$ for aspirin equals $3 \times 10^{-5} .$ If two aspirin tablets, each having a mass of $325 \mathrm{mg},$ are dissolved in a full stomach whose volume is 1 $\mathrm{L}$ and whose $\mathrm{pH}$ is $2,$ what percent of the aspirin is in the form of neutral molecules?
Aspirin has the structural formula At body temperature $\left(37^{\circ} \mathrm{C}\right), K_{a}$ for aspirin equals $3 \times 10^{-5} .$ If two aspirin tablets, each having a mass of $325 \mathrm{mg},$ are dissolved in a full stomach whose volume is 1 $\mathrm{L}$ and whose $\mathrm{pH}$ is $2,$ ...
5 answers
Problem II: For each non-negative integer , n, let Fn be the n-th Fermat number s0 that Fn =22" +1. If m and are distinct non-negative integers, prove that gcd(Fm, Fn) =1.
Problem II: For each non-negative integer , n, let Fn be the n-th Fermat number s0 that Fn =22" +1. If m and are distinct non-negative integers, prove that gcd(Fm, Fn) =1....
5 answers
Coasider theindelmite intcenlj;-; &x (0) (10 pts) Use substitution with u = x ~ 1o cvahate this integnl(6) (I0 pts) Use long division [0 evalate this inlegnl(5 pEs) hhou;h !otian" #ot the TMA" etpLi whythey 4e toth cuntt
Coasider theindelmite intcenlj;-; &x (0) (10 pts) Use substitution with u = x ~ 1o cvahate this integnl (6) (I0 pts) Use long division [0 evalate this inlegnl (5 pEs) hhou;h !oti an" #ot the TMA" etpLi whythey 4e toth cuntt...
5 answers
228. f- dtt +3 3t
228. f- dtt +3 3t...
5 answers
Extra Credit [2 Points]:How does friction affect Newton's second law of motion? Is Newton's Second Law 'still valid with friction ON?
Extra Credit [2 Points]: How does friction affect Newton's second law of motion? Is Newton's Second Law 'still valid with friction ON?...
5 answers
E 6 1 BMe 1 1 1 1 { 1 1 L [1
E 6 1 BMe 1 1 1 1 { 1 1 L [ 1...
4 answers
Question 8 Not yet answered Marked out of 7Flag questionA closed surface with dimensions a=b-0.40 m and c=0.60 m is located as in the figure below: The left edge of the closed surface is located at position X= a. The electric field in the region is non-uniform and is given by E-(3.0+ 55x2 ) iNJC, where x is in meters. Calculate the net electric flux leaving the closed surface?Select one: OA 7.39B. 5.28C.12.89D. 1.76E. 18.39
Question 8 Not yet answered Marked out of 7 Flag question A closed surface with dimensions a=b-0.40 m and c=0.60 m is located as in the figure below: The left edge of the closed surface is located at position X= a. The electric field in the region is non-uniform and is given by E-(3.0+ 55x2 ) iNJC, ...
5 answers
Consider the following standard biochemical free energies released upon hydrolysis of various phosphorylated compounds Which compound contains enough free energy to phosphorylate ADP in the following reaction? ADP ATP (4 G" +35 Kmol)B-P = 8 + Pi (4C" 25 kJlmol)RP =R+Pi 0C" +36 Wlmol)EP +E Pi (DC" 36 kllmol)JP =J+Pi (4G" +35 kllmol)Tc +Pi (AG" 35 kllmol)
Consider the following standard biochemical free energies released upon hydrolysis of various phosphorylated compounds Which compound contains enough free energy to phosphorylate ADP in the following reaction? ADP ATP (4 G" +35 Kmol) B-P = 8 + Pi (4C" 25 kJlmol) RP =R+Pi 0C" +36 Wlmol...
5 answers
Looking t0 the following structures OHOHOHIlhe compound(s) that undergo nucleophilic addition reaction is (are) Choose;TThe compound that have the highest boiling point isChooseThelcompound(s) that gives E upon oxidationChoose;Tne sampounaks) that undergo electrophilic addition reaction is (are) Choose_"NKz
Looking t0 the following structures OH OH OH Ilhe compound(s) that undergo nucleophilic addition reaction is (are) Choose; TThe compound that have the highest boiling point is Choose Thelcompound(s) that gives E upon oxidation Choose; Tne sampounaks) that undergo electrophilic addition reaction is (...

-- 0.056485--