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.

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