Solve by determining the general form the function might take and then evaluating some coefficients. dy/dt+2y=exp (5t)

since it is a first orderedlinear ODE first we look for M (t) = e^integral (2) = e^2t then multiplying whole equation by M will give d[ (e^ (2t)) * y]/dt=e^ (5t) * e^ (2t) d[ (e^ (2t)) * y]=e^ (7t) dt integrating both sides gives (e^ (2t)) * y = (e^ (7t)) / 7 + C solving the result for y gives y = (e^ (5t)) / 7 + C (e^ (-2t)) that is the general solution of the diff. equ.