Solve the following differential equations :

(i) If a differential equation is ,


then y(I.F) = ∫Q.(I.F)dx + c, where I.F = e∫Pdx


(ii) ∫dx = x + c





given:



This is a linear differential equation, comparing it with



P = 1, Q = sinx


I.F = e∫Pdx


= e∫dx


= ex


Solution of the equation is given by


y(I.F) = ∫Q.(I.F)dx + c


y ex = ∫sinx. ex dx + c




12