Solve the following differential equations :

Formula:-

(i) if a differential equation is ,

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

(ii) ∫dx = x + c

This is a linear differential equation, comparing it with

P = 2, Q = 4x

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) = ∫4x.e^2x dx + c

⇒ y(e^2x) = 4(x∫e^2x dx– ∫ ( ∫e^2x dx)dx) + c

using integration by part