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Question: Why 'dsolve' of a simple 1st order ODE with Dirac function returns an incorrect solution?

Question:Why 'dsolve' of a simple 1st order ODE with Dirac function returns an incorrect solution?

EB1000 35 Maple 2022
ode dsolve differential-equations dirac
September 14 2023
1

Hi

On the latest Maple 2022 version, using dsolve with 1st order ODE and Dirac function returns an incorrect solution

dsolve({D(y)(t) + y(t)/tau = Dirac(t)/tau, y(0) = 0})

See attached image. The correct impulse response should be :

y(t) = exp(-t/tau)*Heaviside(t)/tau

The returned solution is 0 for t = 0 and scaled by a 1/2 for t > 0. I never had such an issue with older Maple versions. Is this a bug or am I doing something wrong

Here is the expected solution followed by the Maple solution:
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