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

= e^x

Solution of the equation is given by

y(I.F) = ∫Q.(I.F)dx + c

⇒ y e^x = ∫sinx. e^x dx + c