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:

Here is the code I tried:

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)
print(latex(solution))

The result as latex: {\left(e^{t} \int t e^{\left(2 \, t\right)} H\left(t - 3\right)\,{d t} - \int t e^{\left(3 \, t\right)} H\left(t - 3\right)\,{d t}\right)} e^{\left(-3 \, t\right)} + 6 \, e^{\left(-2 \, t\right)} - 4 \, e^{\left(-3 \, t\right)}

I expected that the solution would not contain integrals