1)Find the general solution of

. 2)Determine the solution that satisfies

,

.

Attempt: 1)I've found the general solution to the homogeneous DE to be

and

.

So I propose a solution to the non-homogeneous DE to be of the form

.

. Similarly,

.

Therefore the general solution to the DE is of the form

. Should I calculate the indefinite integrals or just let it this way? What method would you use to solve the integrals? (I don't see any good u/substitution nor integration by part).

2)I think I should replace t with 0 in my last expression and then equal to 0. But I'm totally unsure about the limits of the integrals. To get

, I would derivate

with respect to t, set

and equal

in order to get the constants of integration if they are indefinite integrals? I'm confused on this.