(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 = 2, Q = sinx

I.F = e^∫Pdx

= e^∫2dx

= e^2x

Solution of the equation is given by

y(I.F) = ∫Q.(I.F)dx + c

⇒ y e^2x = ∫sinx. e^2x dx + c