Finding general solution

Given that three solutions to the inhomongenous DE equation y''+p(t)y'+q(t)y=g(t)

are y1=1+e^(t^2), y2= 1+te^(t^2), y3= 1+(t+1)e^(t^2),

find the general solution

Since , and all satisfy the ODE then

and

satisfy



Thus, the general solution is

.

Note that we could have used either for but can adjust the constants such that all we need is .

Why did you subtract the solutions? Thanks

It was to get to the homogeneous ODE

If and satisfy your ODE, i.e.



and



then substracting gives

.