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 = 1, Q = e^–2x

I.F = e^∫Pdx

= e^∫Pdx

= e^x

Solution of the equation is given by

y(I.F) = ∫Q.(I.F)dx + c

⇒ y(e^x) = ∫e^–2x e^x dx + c

⇒ y(e^x) = ∫e^–x dx + c

⇒ y(e^x) = –e^–2x + c

⇒ y = –e^–2x + c e^–x