Find the general solution for the following differential equ

Find the general solution for the following differential equation: dy/dy = -2y - 5t.

Solution

y\' + 2y = -5t

=>
y\'(e^2t) + 2y(e^2t) = -5te^(2t)

=>

d(ye^2t) = -5te^(2t)dt

=>

ye^2t = (-5/4) e^(2t) (2t-1) +c

=>

y = (-5/4)(2t-1) + ce^(-2t) = ce^(-2t) -5t/2 + 5/4