Solve the differential equation

Given

This is a first order linear differential equation of the form

Here, and Q = 3x

The integrating factor (I.F) of this differential equation is,

We have

[∵ m log a = log a^m]

∴ I.F = x^–1 [∵ e^{log x} = x]

Hence, the solution of the differential equation is,

We know

⇒ yx^–1 = 3x + c

⇒ yx^–1 × x = (3x + c)x

∴ y = (3x + c)x

Thus, the solution of the given differential equation is y = (3x + c)x