I've been trying to get Sage to solve an ODE using Laplace transforms. Unfortunately, shifted functions appear to cause a problem for the inverse_laplace command. David Joyner's ODE book (dated 2008) says that Sage does not have the functionality to do this. Has this situation changed? Do I need to do something differently here to get this to work?
Here is a snippet of something I tried.
u=piecewise([[(0,3),0],[(3,infinity),exp(-2*(t-3))]],t)
u.laplace(t,s)
inverse_laplace(_,s,t)The first two lines work properly, but the last line returns a formal result:
ilt(e^(-3*s)/(s + 2), s, t)