Find the solution to the differential equation as same way as example question

1 . Find the solution to the differential equation y'thy = ex-2 Solve this Problem 1. Find the solution to the differential equation y' + 2y = 2r. example We use integrating factor as the differential equation is of the form: y' ( x ) + p(x ) . YLx ) = g(x ) where P(X) = 2 , 9 ( x ) = 2x Acx) = e jp(x) dx = e 2 X e 2X y' + e 2 x 2 4 = ez x 2 X ( y . e 2 x )' = 2e P 2 x X 4. e 2x = 2 S ezx . x d x 2x . X dx U - X V = ze2x = z x e2x - 25 e2x dx du = dx dv= ezx dx = zkez x - 2 . zex +c y . e 2x = xe zx _ ze 2x + c y = X- It c. e - 2 x