Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

What is the differential equation for $$ y=c_1e^{2x}\sin x + c_4 e^{2x} \cos x - xe^{-x}. $$ I'm not sure how to incorporate the last part of the solution into solving this problem?

share|improve this question
1  
A related problem. –  Mhenni Benghorbal Feb 28 at 3:19
    
Please do not change the question after it has been answered. –  Joel Reyes Noche Feb 28 at 3:33

1 Answer 1

up vote 2 down vote accepted

Question: find differential equation for which $y = c_1+c_2x+c_3e^{2x}\cos(x)+c_4e^{2x}\sin(x)-xe^{-x}$ forms the general solution.

Solution Sketch: Well, it is fourth order with $\lambda = 0,0,2\pm i$ and so $L=D^2((D-2)^2+1)$ and $L[y]=g$ is the differential equation. Now the question is what is $g$ if $L[-xe^{-x}]=g$? I think you can figure that out if you can differentiate. Yes?

share|improve this answer
    
Yes, thank you. –  Ali Mubashir Feb 28 at 2:19
    
Glad to help, interesting question. –  James S. Cook Feb 28 at 2:25
    
This answer refers to the original version of the question. For some reason, the OP changed the question (removed the first two terms in $y$). –  Joel Reyes Noche Feb 28 at 3:32
    
@JoelReyesNoche indeed, it is for your implicit concern that I added the first two lines to my answer. –  James S. Cook Feb 28 at 13:32

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.