Find a particular solution y_p for the ODE
x" + 9x = g(t)
where g(t) = 1 0<t<1/2
0 1/2<t<1
Assume that when g(t) is extended to the negative t
axis in a periodic manner, the resulting function is
even.
Have a look at example 4 here
Pauls Online Notes : Differential Equations - IVP's With Step Functions