Laplace transform not found.

I am trying to compute the Laplace transform of a known function. I have replicated the code shown below in Mathematica and it works fine, but I am unsure as to why it is not working in Matlab. The result I get is just laplace (some expression).

clearvars
close all
syms G w0 wc wk tau s C
a(tau) = int(wk^3*exp(-1i*(wk-w0)*tau), wk, 0, wc);
corr(tau) = (G/(w0^3))*(a(tau));
F(s) = laplace(corr(tau),tau,s);
C(s) = solve(s*C-1==-F(tau)*C,C);

[Walter Roberson]

How are you doing the transform in Mathematica? Wolfram Alpha says it is invalid.

https://www.wolframalpha.com/input/?i=laplace+transform&assumption=%7B%22F%22%2C+%22LaplaceTransformCalculator%22%2C+%22transformfunction%22%7D+-%3E%22%28G*%28%286*exp%28tau*w0*sqrt%28-1%29%29%29%2Ftau%5E4+%2B+%28exp%28tau*w0*sqrt%28-1%29%29*exp%28-tau*wc*sqrt%28-1%29%29*%28tau%5E3*wc%5E3*sqrt%28-1%29+%2B+3*tau%5E2*wc%5E2+-+tau*wc*6*sqrt%28-1%29+-+6%29%29%2Ftau%5E4%29%29%2Fw0%5E3%22&assumption=%7B%22F%22%2C+%22LaplaceTransformCalculator%22%2C+%22variable1%22%7D+-%3E%22tau%22&assumption=%7B%22C%22%2C+%22laplace+transform%22%7D+-%3E+%7B%22Calculator%22%7D&assumption=%7B%22F%22%2C+%22LaplaceTransformCalculator%22%2C+%22variable2%22%7D+-%3E%22s%22

[Jose Aroca]

Hi, thank you for your answer! I am not sure how that online solver works, but this works just fine in Mathematica! I have attatched and image of the code as it gets real messy whe trying to write it here.

Answer 1

[Walter Roberson]

The wk^3*exp(x*tau) is getting integrated to include a /tau^4 term -- the general pattern wk^n*exp(...*tau) integrates to something that divides by tau^(n+1)

And that is leading to a problem with the laplace. You do not have compensating tau^4 in your numerator, and

syms t s
laplace(1/t, t, s)

which is to say that the laplace transform of division by the variable being transformed is not being processed. That is because the transform does not exist.

https://math.stackexchange.com/questions/147126/laplace-transform-of-1-t

[Jose Aroca]

I don't understand. If the Laplace tranform does not exist why is Mathematica solving it without problems?