I would like to solve a simple 2nd-order ODE with one of the boundary conditions defined at $ -\infty $. The ODE I am looking to solve is:
$$ w''(z)-2i\pi^2w(z)=0 $$
with the corresponding boundary conditions:
$$ w(z=-\infty)=0, \; w'(z=0)=0+i\dfrac{\tau_{0}}{\mu}. $$
My attempt at a solution using DSolve
is as follows:
DSolve[{-2 I \[Pi]^2 w[z] + (w^\[Prime]\[Prime])[z] == 0,
w[-Infinity] == 0, w'[0] == 0 + I Subscript[\[Tau], 0]/\[Mu]}, w[z],z]
but I only get an empty set of curly brackets as an output. I checked the rest of my snipet of code without the w[-Infinity]==0
boundary condition, and that works as expected; therefore, I know that this is a problem with the boundary condition at $z=-\infty$. I am looking for methods with which I can solve simple ODE's with boundary conditions at infinity, and any help would be greatly appreciated.
w
or onw'
? You have it both ways. $\endgroup$