5

I) Solve the given differential equations by undetermined coefficients-superposition approach (10 points) y" 2y' _ 3y = r2 _ 2 + re2r_ 15 points) y" ...

Question

I) Solve the given differential equations by undetermined coefficients-superposition approach (10 points) y" 2y' _ 3y = r2 _ 2 + re2r_ 15 points) y" 4y + 8y (32 xlez cos 2r + (10z? 1)e2r sin 2.

I) Solve the given differential equations by undetermined coefficients-superposition approach (10 points) y" 2y' _ 3y = r2 _ 2 + re2r_ 15 points) y" 4y + 8y (32 xlez cos 2r + (10z? 1)e2r sin 2.



Answers

Solve the given differential equations. $$y^{\prime \prime \prime}-y^{\prime}=\sin 2 x$$

In the problem they have been given they the square white minus four while that equals two cynics plus two. Cossacks. Now in the problem this is ordinance mm squared minus for that. It was true. So it is M-plus two and two M -2. That equals to zero. So further we have M. to end -2. So Complimentary solution becomes I see that is equal to c. one into the power -2 weeks plus C. To eat the power to X. Or wipe equals uh Sin X plus B. Cossacks. Therefore the white becomes a Cossacks minus B. Cynics. Or further, the square wipe is equal to minus a cynics minus B. Cossacks. So you have to put these values in this equation. The first equation. So here we have the square wipe minus four wipe that equals two minus a cynics minus B. Cossacks -4. Into a cynics plus B. Cossacks. Therefore it is equal to minus five. Sin X -5 B. Cossacks. Now you have to compare this coffee since of this and this. Therefore we have -5 that equals to one and -5 B. That equals to two. So a. is equal to -1 upon five And B is equal to minus to a .5. And further we have the values of A. And B. So we put the values In the total equation or a solution. That is why that equals two. Why C plus wipe that is equal to. So you went into the power -2 weeks plus C. To eat the power to x -1 upon five Cynics -2 upon five Cossacks. So this is the answer to the problem.

So start this problem. A song for the homogeneous equation. So I have the R squared minus r minus two equals zero. And we can factor this to be our plus one Times are -2 equals zero. And so of our values, sorry, our values negative one and two. And so with this we can actually build a homogeneous ocean. Homogeneous ocean is going to see one each of the negative X plus C. To eat a two X. And we can also take a guess at our particular solution, sort of particular solution. It's gonna be a co sign X plus the syntax. And we'll need to take through this twice. So Y P prime is going to be negative A co sign sorry, negative A sign X plus B. Cosine X. And YP double prime is going to be negative A cosign X minus B syntax. And so we need to plug this into our original equation. So we'll have that Y double prime negative A Cosign X minus B. Synnex minus Y. Prime. So plus a syntax -7. Cosine, X minus two times Y. So minus two times a cosign X minus to be Synnex All equals to two Synnex. So simple this simplify this down a little bit before we try and build a system of equations here. So we have like terms here and here. We also have like terms here and here and that's about it. And so we can simplify this down to be negative three. A cosign X A -3 B. Synnex plus a Synnex minus PICO Xanax Equals to two syntax. And so now we can actually build our systems of equations. So let's start off with the coastline terms. We'll have these two has been co signed terms so we'll have negative three A minus B equals zero. Our second equation is going to be the sign terms, so we'll have you. And then then we can build the equation negative three B Plus a equals to two. So now that we have a system of equations, let's try and solve them. So let's organize it a little bit more. We'll have negative three B Plus a equals to two. And on the bottom will have negative B minus three A equals to zero. So it's multiply the bottom by three. So I have that native three B plus A equals to two. And in the bottom will have negative three B -9 A equals zero. And so it's let's subtract these terms here. So if we subtract the bees cancel out And we'll end up adding these two terms here. So the 10 a. Equals two Where the aid goes to 1/5. And so now we can also um sulfur be by plugging this A value in two original equations. So negative three A. In this case we said that A. Is 1/5 -7 equals zero. So negative 3/5 minus B equals to zero. If we subtract 3/5 well or rather add 3/5 we'll have that negative B equals 2 3/5. And if we multiply by negative one on both sides will have that be Equals -3/5. And so with this we can actually build our particular solution. So a particular solution is going to be EKO Synnex. So 1/5 cosign X plus PICO Synnex which is negative three fists syntax. And we can also build our total solution which consists of our modern institution plus or particular solution. In this case we said our motion insufficiency one eats the negative X plus C. Two Eat the two x. We're gonna add our particular solution. So we have that plus 1/5. Cosign axe -3 5th syntax. And that's your answer.

Question too. I am one devil Prime mine Green. Why ride you will sign of two X. My wider crime becomes R squared minus three are equal. Zero is my equation. Factoring out the r, they are minus three equals zero r equals zero or three. There were my general equation. To start with, C one need to the three x plus c two he to the zero x zero. Anything to the zero powers one. So I have seen one either the three x plus c two. I'm gonna focus my attention on my subpoena equation, and I have wise p of X is going to equal a two x left. The sign to X There were white crime would equal to a negative to a sign to excite captain for that chain rule for trick. So I have to you you cry and then I have That's to be, oh, sign to X and then my wife that will prime derivative of Sinus courtside Negative for a Jane Roe again, who's trying to x minus derivative of coast and negative sign for the sign. U x So in my general, in my wide double crime every time they see double pregnant. Gonna put this equation my double prime. Why? Double prime. It's gonna start off with negative four and sighing u X minus four Sign two X minus three. Why crime is this equation more negative too, eh? Sign? Well, I have two picks. Be thanks equal. Oh, that's distributing my negative three. I have a negative for a why, it's for the sign two x six A sign X line six necks equal flying I'm gonna pull out my co sign and my signs like the ex is the negative for a 96 My sign of two eggs And that gives me negative for B That's six. A home to ex their whole or negative or B plus. It's a has won and negative for a minus six B c on cedar. So negative four B minus six A equals one and thanks. Um B a near 40 Anything for you and negative worry minus its He looks here. So now I saw my system of linear equation, and I am going to multiply the top number by negative three. So I get while b minus 18 a equals negative three. And I'm gonna multiply the bottom. Why two? So get negative. 12 B minus a a equal. See rail. My bees cancel as I get negative. 26 A equals negative. Three A equals three over 26. And then I put that back into my equation, and I have negative forward less six times Read. Actually, I'm gonna use the other equation. Really cool. See road look easier. Negative. Six B minus who were really over 26 row. So negative six bean equals well over 26 and then multiply both sides by a negative 16 And I get being eaten. Make it is Well, thank you to Negative too. Over 26 negative. One teen. So our general equation that we started with age have one e to the three. X c two. Yes. Three 26. Co sign two x less minus one. They're mean. Sign two months. Yes, General

So in this equation, we can see that. Well, I we have em over here, which is going to be two x 222 x times y plus coastline lie, um, and we're going to have end, which is going to be X squared minus x times sign why minus two. Acts that to why? And I'm just going to fix that to a little bit. Um and so when we take the derivative of both of them, we will see that they are indeed, in fact, So now we're going to take the integral of em with respect to D X. And when we do this, we're going to be getting X square times why plus x Times co sign lie. And when we do the same thing for an we're going to get well, with respect to DX, we're going to get X actually, Oops, my bad. Not DX. When we do this, when we do it with when we do it with respect to ah de y, we're going to get X squared times. Why, that's a bad by. Let me just, uh, fix that up a bit minus x squared. Actually, no, not X squared my bed good minus. It's going to be actually plus co sign plus x times cosign y and it's going to be minus Why squared? And so when we self But we have the equation and self asi we're going to have X squared times why? Plus and we just crossed the soft because we really had both of these plus x times co sign why? And we're gonna cross this off and we're going to subject this by why squared?


Similar Solved Questions

5 answers
Molecalax oxIde aeQUtntcn lonic ejualion reduce and speaics of Cuts) t CgNOskas 2) 2he) + Cu_ (n6) Cad > Mgc) + an (No,J2caa ~ 4) Cucs) + Hcl tad S )z nus) + HCltac) ~
Molecalax oxIde aeQUtntcn lonic ejualion reduce and speaics of Cuts) t CgNOskas 2) 2he) + Cu_ (n6) Cad > Mgc) + an (No,J2caa ~ 4) Cucs) + Hcl tad S )z nus) + HCltac) ~...
5 answers
Straight line surprisingly nonh eas speed = of 2 mls in & at an angle of 30" deck at & walks and across boate distracted and detenine 5 magnitude - drunken- walk 'sailor= then gets time interval: sailor = does seconds The seconds. During this nonth_ for due of 1.5 m/s accel leration. with speed sailor" average direction . of the a= a^ 7Js% 20
straight line surprisingly nonh eas speed = of 2 mls in & at an angle of 30" deck at & walks and across boate distracted and detenine 5 magnitude - drunken- walk 'sailor= then gets time interval: sailor = does seconds The seconds. During this nonth_ for due of 1.5 m/s accel leratio...
5 answers
(I pts) Frcvide reascnable mechanisrn to explain the following reaction.[C HJ
(I pts) Frcvide reascnable mechanisrn to explain the following reaction. [C HJ...
5 answers
Calculate the volume of the solid formed by rotating about the line y = I =0. I = In(4) , y and the graph of ythe region boundedSet up but do not evaluate the integral that gives the arc length of the graph of y tan(~) on [-7/4,7/4.
Calculate the volume of the solid formed by rotating about the line y = I =0. I = In(4) , y and the graph of y the region bounded Set up but do not evaluate the integral that gives the arc length of the graph of y tan(~) on [-7/4,7/4....
5 answers
The compound from the following list that exhibits the infrared spectrum below is (Use YOur cursor to read the IR frequency scale )H-C=C Ohc,c+s CH(CHh-C=c-HFlash Installation and Troubleshooting Infrared spectra provided countesy Thermo Electon Corp 110%1 Wavenumber:0% 4000 350030002500 2000 Wavenumber (cm"15001000Use Your cursor t0 read the frequency scale of this spectrum:
The compound from the following list that exhibits the infrared spectrum below is (Use YOur cursor to read the IR frequency scale ) H-C=C Ohc,c+s CH(CHh-C=c-H Flash Installation and Troubleshooting Infrared spectra provided countesy Thermo Electon Corp 110% 1 Wavenumber: 0% 4000 3500 3000 2500 2000 ...
5 answers
Required IntormationWhich of the following muscles is not part of the pelvic outlet region?Multple Choicebulbospongiosus{uperficial transverse perineaScerccovetnobesPrey
Required Intormation Which of the following muscles is not part of the pelvic outlet region? Multple Choice bulbospongiosus {uperficial transverse perinea Scerccovetnobes Prey...
5 answers
Question 86 ptsDifferentiate: f (2) = Vz? +1(2) =(2) =f' () = (? +1)} (2) =f' (2) = 2cVz? +1Question 96 ptsDetermine dy for the implicit equation .? + ys =xCOS y 612c+ cOS y 3y2 4 2 sin y3y2 4 sin y 2I+I cOS y2t+cos Ty 3y2 +sin #ydrdy dr3y2 +sin ydy dZ3y2 +x sin y-% COS y
Question 8 6 pts Differentiate: f (2) = Vz? +1 (2) = (2) = f' () = (? +1)} (2) = f' (2) = 2cVz? +1 Question 9 6 pts Determine dy for the implicit equation .? + ys =xCOS y 61 2c+ cOS y 3y2 4 2 sin y 3y2 4 sin y 2I+I cOS y 2t+cos Ty 3y2 +sin #y dr dy dr 3y2 +sin y dy d Z 3y2 +x sin y-% COS y...
5 answers
Use the compound interest formulas A= P(1+3)' and A = Pert to solve the exercises below Round your answer to the nearest cent make sure to include the dollar sign:Find the accumulated value of an investment of S13790 for 4 years at an annual interest rate of 3.4% if the money iscompounded semiannually: compounded quarterly: compounded monthly: compounded continuously:dollarsdollars2 dollars2 dollars
Use the compound interest formulas A= P(1+3)' and A = Pert to solve the exercises below Round your answer to the nearest cent make sure to include the dollar sign: Find the accumulated value of an investment of S13790 for 4 years at an annual interest rate of 3.4% if the money is compounded sem...
5 answers
Tutorial ExerciseFind the sum of the series. (-1)" #2u 22" (")iPart 1 of 3We know that coS X(-1)n
Tutorial Exercise Find the sum of the series. (-1)" #2u 22" (")i Part 1 of 3 We know that coS X (-1)n...
5 answers
Cables AC and BC are alached to points A and Brespectively Js Shown These tWo cables &re then tled together polnt C to support Jofo nt load. Detcrmine the tension In cable DC Give Your answer in ncwtons (WJond torndto thantaratnexton7507501960 N
Cables AC and BC are alached to points A and Brespectively Js Shown These tWo cables &re then tled together polnt C to support Jofo nt load. Detcrmine the tension In cable DC Give Your answer in ncwtons (WJond torndto thantaratnexton 750 750 1960 N...
5 answers
Continuous random variable X has a paf = of the form: f(x) (107/594) x^3, for .82 < X < 2.40. Calculate the standard deviation (sigma) of XYanitiniz:0.3380.4810.2510.5230.0680.5305060.1390.1150.164
continuous random variable X has a paf = of the form: f(x) (107/594) x^3, for .82 < X < 2.40. Calculate the standard deviation (sigma) of X Yanitiniz: 0.338 0.481 0.251 0.523 0.068 0.530 506 0.139 0.115 0.164...
2 answers
2. (5 points) Consider a graph G on n vertices that has one vertex ? of degree k and every other vertex is a path that is adjacent to v (see the picture below) Find the chromatic polynomial of G.vtcHices &ulj' Fav all otlers 0re 0n P-+L acljac6r! Fa V ,
2. (5 points) Consider a graph G on n vertices that has one vertex ? of degree k and every other vertex is a path that is adjacent to v (see the picture below) Find the chromatic polynomial of G. vtcHices &ulj' Fav all otlers 0re 0n P-+L acljac6r! Fa V ,...
5 answers
> A heavy (2-kg) 2-m rope hangs from the ceiling, andhas a 1-kg block attached to the bottom.> What happens to the speed of the wave pulse that travelsfrom the block to the ceiling? > What would you have to do to solve for the time?
> A heavy (2-kg) 2-m rope hangs from the ceiling, and has a 1-kg block attached to the bottom. > What happens to the speed of the wave pulse that travels from the block to the ceiling? > What would you have to do to solve for the time?...
5 answers
A single positive charge rests above cylinder. The cylinder has a radius of cm and Nm Nm- height of 3 cm. For this closed cylinder, #top 15 and bottom What is @walls?
A single positive charge rests above cylinder. The cylinder has a radius of cm and Nm Nm- height of 3 cm. For this closed cylinder, #top 15 and bottom What is @walls?...
5 answers
10 ptsQuestion 41Confidence limit represents a range of values within which the true value- can be expected to be located with a given level of confidence:TrueFalse
10 pts Question 41 Confidence limit represents a range of values within which the true value- can be expected to be located with a given level of confidence: True False...
4 answers
A researcher is investigating differences invictimization rates across northern and southern cities inCalifornia. She collects data and finds that the mean victimizationrate in 5 northern Californian cities is 40.10. The meanvictimization rate for 8 southern Californian cities was 67.85.What would this researcher’s null and alternative hypotheses looklike (be specific)?Please type your answer instead of writing it onpaper.
A researcher is investigating differences in victimization rates across northern and southern cities in California. She collects data and finds that the mean victimization rate in 5 northern Californian cities is 40.10. The mean victimization rate for 8 southern Californian cities was 67.85. What wo...
5 answers
The Evergreen Fertilizer Company produces two types of fertilizers. Fastgro and Super Two. The company has developed the following nonlinear programming model to determine the optimal number of bags of Fastgro () and Super Two (12) that it must produce each day to maximize profit; given a constraint for available potassium: maximize Z = S3011 24} + 25x2 0.543 subject to 3X1 6x2 300 Ib. Determine the optimal solution to this nonlinear programming model
The Evergreen Fertilizer Company produces two types of fertilizers. Fastgro and Super Two. The company has developed the following nonlinear programming model to determine the optimal number of bags of Fastgro () and Super Two (12) that it must produce each day to maximize profit; given a constraint...

-- 0.020072--