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Remove integrals from ODE solved by desolve

I have been working on solving some second order ODE's with desolve. When trying to solve this one with heaviside functions it always returns an answer with integrals. I am trying to have an answer that does not have integrals. Here is the code I am running:

t = var('t')
y = function('y')(t)

equation = diff(y, t, 2) + 5*diff(y, t) + 6*y == t*heaviside(t-3)
solution = desolve(equation, y, ics=[0, 2, 0])
show(solution)