In your numerical solution your integration statement (I am not familiar with Maple or is this sympy where "import sympy as sp" is used) is -

solution_numeric = 1 / sp.pi * sp.integrate(sp.re <http://sp.re>(solution_in_frequency_domain_numeric*sp.exp(sp.I*2*phi*t)),(phi,0,4))

Does that statement mean you are integrating between 0 and 4 and not -infinity to infinity?  If so why did you pick the interval [0,4] to integrate?

Also why only use the real part?  A good check of the calculation is if the imaginary part is zero.

On 2/10/23 11:32 AM, 'Tom van Woudenberg' via sympy wrote:
solution_numeric = 1 / sp.pi * sp.integrate(sp.re <http://sp.re>(solution_in_frequency_domain_numeric*sp.exp(sp.I*2*phi*t)),(phi,0,4))

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