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
= e2x
Solution of the equation is given by
y(I.F) = ∫Q.(I.F)dx + c
⇒ y(e2x) = ∫4x.e2x dx + c
⇒ y(e2x) = 4(x∫e2x dx– ∫ ( ∫e2x dx)dx) + c
using integration by part