Laplace transform of a derivative

[Staffan Lundberg]

I am working with a project to replace Matlab with Python, in a calculus course.

Issue: Current versions of SymPy can not explictliy generate the Laplace transform of a derivative.

This is no problem for Matlab. Let me provide an example. In Matlab code:

syms s y(t) Y

# 1st and 2nd derivative of y wrt t

Dy=diff(y(t),t);
D2y=diff(Dy,t);
laplace(Dy)
laplace(D2y)

# Matlab output::

ans =
s*laplace(y(t), t, s) - y(0)
ans =
s^2*laplace(y(t), t, s) - s*y(0) - subs(diff(y(t), t), t, 0)

This property is crucial when solving  Initial Value Problems without Python's dsolve routine.

I address this issue to SymPy developers. Hope that future SymPy versions will do these calculations.

[Eric Barth]

Hi Staffan,

I'm thinking of switching from Maxima to python in my math classes, and I recently noticed the same issue you're talking about.  

I have a prototype laplace() code that I believe handles derivatives correctly when solving linear IVPs.  

You can read about it at 

https://ejbarth.github.io/PythonMathClassroom/

I'd be very happy to hear from others if this is useful to you.

Eric