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.