Linear ODE with constant coefficients


has a nontrivial constant solution. Find $a_n$.

I've never done anything like this before and I have no clue how to do this. How do I solve this problem? Thanks.

  • 1
    $\begingroup$ What have you tried? Have you tried solving it for $n = 1, 2, 3...$? Do you see a pattern? It really helps to share your thoughts and what you have done to get an idea of where you are at. Regards $\endgroup$ – Amzoti Oct 2 '13 at 2:19
  • $\begingroup$ I know $a_n$, $a_{n+1}$, etc. are supposed to be constant. Does that mean $a_n$ has infinite solutions? $\endgroup$ – user91971 Oct 2 '13 at 12:28

A nontrivial constant solution means that there is a function $y$ which

  1. satisfies the equation
  2. is constant
  3. that constant is not zero

All derivatives $y'$, $y''$, etc of a constant function are equal to $0$. Therefore, the equation takes the form $$a_0 \cdot 0+a_1 \cdot 0+ \cdots + a_{n-1} \cdot 0+ a_n y = 0$$ Simplify this. Recall that $y$ is not zero. Make your conclusion about $a_n$.

  • $\begingroup$ Ah, I see. Thanks! $\endgroup$ – user91971 Oct 3 '13 at 1:16

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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