How to find solution of ODE $x''(t)+e^{t^2} x(t)=0$, for $ t\in[0,3\pi]$. I am not getting any hint. Please give some hint.
solution of ODE $x''(t)+e^{t^2} x(t)=0$, for $t\in[0,3\pi]$
2
$\begingroup$
ordinary-differential-equations
-
4Possible duplicate of [solution of ordinary differential equation $x''(t)+e^{t^2} x(t)=0, for t\in[0,3\pi]$](http://math.stackexchange.com/questions/2148589/solution-of-ordinary-differential-equation-xtet2-xt-0-for-t-in0-3) – 2017-02-18
-
1not a duplicate cause last time they asked about the number of zeros, not for a solution. (The first is a better question.) – 2017-02-18
-
0There is not even a symbolic solution for the simpler Airy equation $y''+ty=0$, you can not expect to find a symbolic solution in this case. And as the equation is highly oscillating, with at least $373791673$ roots in this interval, also numerical solutions will be hard to come by. – 2017-02-18
-
0@Moo : No specific math tool except a calculator. The number is from my answer in the other question using the Storm-Picone comparison theorem. One can even go further, any solution on the interval $[2.9π,3π]$ has at least $10^{17}$ roots inside that interval, as $e^{(2.9π)^2/2}=1.0567..·10^{18}$ is a lower bound for the frequency on that interval. – 2017-02-18