Differential equation and discrepency

I initially assumed that there are q(x) and p(x) which continues on the interval, and I defined initial conditions. f(0)=0 and f'(0)=0. Still, I can't get to a discrepancy with the existence and uniqueness theorem. I would be glad to have a little help here.

Prove that there is no continues functions $p(x),q(x)$ on the interval $(-2024,2024)$ such that: $y''+p(x)y'+q(x)y=0$ and  $f(x)=\int_{0}^{x^{2024} }e^{-t^{2} }dt$ is a solution to the equation .


Answers can only be viewed under the following conditions:
  1. The questioner was satisfied with and accepted the answer, or
  2. The answer was evaluated as being 100% correct by the judge.
View the answer
  • This was a challenging problem and it took me much longer than I expected. I spent about a couple of hours on this. I would appreciate a tip.

  • I think you have a mistake in the derivative it should be x^6070.

    • Yes, I corrected the answer.

The answer is accepted.
Join Matchmaticians Affiliate Marketing Program to earn up to a 50% commission on every question that your affiliated users ask or answer.