Laplace Transfer Functions Solved with Python

Solve for the symbolic and analytic solution for transfer function problems with Python. Two packages are Sympy (symbolic solution) and GEKKO (numeric solution). The advantage of a symbolic (analytic) solution is that it is highly accurate and does not rely on numerical methods to approximate the solution. Also, the solution is in a compact form that can be used for further analysis. Symbolic solutions are limited to cases where the input function and system transfer function can be expressed in Laplace form. This may not be the case for inputs that come from data sources where there the input function has random variation. A symbolic solution with Laplace transforms is also not possible for systems that are nonlinear or complex while numeric solvers can handle many thousands or millions of equations with nonlinear relationships. The disadvantage of a numeric solution is that it is an approximation of the true solution with possible inaccuracies. Another disadvantage is that solvers may fail to converge although this is not typical on problems with an analytic solution.

[pnachtwey]

I use symptom to generate equations for other computers. Usually I use the solver. I do simulations numerically.

[delavar]

It seems that inverse_Laplace_transform is very much limited. I could not find inverse of G3.
G1=1/(s**2+4)
G2=(3*s+1)*exp(-3*s)/s**2
G3=G1*G2

[importantbiology]

Please code seen clear or code PDF share in your description box.