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

Here,

This is a linear differential equation, comparing it with

P = 2, Q = 6e^x

I.F = e^∫Pdx

= e^∫2Pdx

= e^2x

Solution of the equation is given by

y(I.F) = ∫Q.(I.F)dx + c

⇒ ye^2x = ∫6e^x e^2x dx + c

⇒ ye^2x = ∫6e^3x dx + c

⇒ ye^2x = 2e^3x + c

⇒ y = 2e^3x + ce^–2x