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.

Let's say we have a linear ODE with polynomial coefficients $p_j(x)$: $$ p_n(x) y^{(n)}(x)+\dots+p_1(x)y'(x)+p_0(x)y=0 $$ and let's say $x_0$ is a root of $p_n(x)$. What can be said about uniqueness of the IVP for this ODE at $x_0$? In particular, if I succeeded to prove that an analytic solution $y_0(x)$ satisfies $y_0(x_0)=y'(x_0)=\dots=y^{(n-1)}(x_0)=0$, does it necessarily follow that $y_0(x)\equiv 0$?

share|improve this question

1 Answer 1

up vote 2 down vote accepted

No. Consider Cauchy problem $xy'-y=0\;$, $y(0)=0\;$. It has solutions $y=Cx\;$, $\ C\in\mathbb R\;$.

share|improve this answer

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.