Advanced Search

Question: How to add exponent patterns for inverse Laplace transform

Question:How to add exponent patterns for inverse Laplace transform

Honigmelone 102 Maple 2024
inttrans invlaplace
10 hours ago
0

Hi

I want to add this rule to maple invlaplace:

invlaplace(Divide[exp(-s*a),b*Power[s,2] +c)]) - Wolfram|Alpha

It works on expressions that use "exp(-s*a)" but not on expressions with "e^(-s*a)". I do not know how to force maple to substitute the expressions and I do not know how to formulate this rule to make it stable. I need this functionality since maple returns results with e^(...) instead of exp(...). Can you please help me? I have attached a workbook example.

> 

restart;with(inttrans)

[addtable, fourier, fouriercos, fouriersin, hankel, hilbert, invfourier, invhilbert, invlaplace, invmellin, laplace, mellin, savetable, setup]

 (1)
> 

addtable(invlaplace,exp(-s*a)/(b*s^2+c),Heaviside(t - a)*sin(sqrt(c)*(t-a)/sqrt(b))*1/(sqrt(b)*sqrt(c)),s,t,a,a::positive)
> 

addtable(invlaplace,e^(-s*a)/(b*s^2+c),Heaviside(t - a)*sin(sqrt(c)*(t-a)/sqrt(b))*1/(sqrt(b)*sqrt(c)),s,t,a,a::positive)
> 

 

> 

assume(a_pos::positive)
> 

invlaplace(exp(-s*a_pos)/(b*s^2 + c), s, t)

Heaviside(t-a_pos)*sin((c/b)^(1/2)*(t-a_pos))*(c/b)^(1/2)/c

 (2)
> 

invlaplace(e^(-s*a_pos)/(b*s^2 + c), s, t)

invlaplace(e^(-s*a_pos)/(b*s^2+c), s, t)

 (3)
> 

 

> 

algsubs(e^=exp,e^c)

Error, symbol unexpected

  

NULL

Download inttrans_exponent_question.mw

Thanks!

edit: simplified example
Please Wait...