GUESS one function which solves the problem below, by determining the general form the function might take and then evaluating some coefficients. dy/dt+2y=exp(5t)

Question

GUESS one function  which solves the problem below, by determining the general form the function might take and then evaluating some coefficients.  dy/dt+2y=exp(5t)

anonymous · Answer

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.