Question

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

Answer 1

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.