Solve the following differential equation:

Given,

⇒

⇒

⇒

This is a linear differential equation. Comparing with the standard form

A solution of such equation is given by:

y(I.F) = where I.F = integrating factor

We get P(x) = & Q(x) = 3x

Integrating factor I.F is given :

∴ I.F =

We know that:

∴ I.F =

⇒ I.F =

We know that:

∴ I.F = 1/x

∴ The solution is given as:

⇒

⇒

⇒ y = 3x² + Cx