Solve the following differential equations :

xdy = (2y + 2x⁴ + x²)dx

(i) If a differential equation is ,

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

Given:-

This is a linear differential equation, comparing it with

,

Q = 2x³ + x

I.F = e^∫Pdx

= e^–2logx

=

Solution of the equation is given by

y(I.F) = ∫Q.(I.F)dx + c