Find the solution to the differential equation

1. Find the solution to the differential equation y'+ ty= ex-2Problem 1. Find the solution to the differential equation y' + 2y = 21. We use integrating factor as the differential equation is of the form: y' ( x ) + p(x ) . y(x ) = g(x ) where P(X ) = 2 , 9 ( x ) = 2x Acx ) = p JP(x) dx = e 2x e 2 x y'+ e 2 x 2 4 2 X ( y. e 2x ) = ze 2x X 4. ezx 2 S e2x. x dx sezx . X dx U - X V = ze2x = 2 x e2x - 25 exx dx du = dx dv= e 2x dx = zxe2x - 2 . 2 02x + c y . ezx xe zx - ze2x + c y = X- It ce - zx