Solve the differential equation $(4+t^2) \frac{dy}{dt} + 2ty = 4t$

Question

Solve the differential equation $$(4+t^2) \frac{dy}{dt} + 2ty = 4t$$

Solution:

$$(4+t^2) \frac{dy}{dt} + 2ty = \frac{d}{dt}[(4+t^2)y]$$

How?

Here's what I did:

$$\frac{d}{dt}[(4+t^2)y] = 4t$$

Then we integrate both side:

$$(4+t^2)y = 2t^2 + c$$

$$y = \frac{2t^2+c}{4+t^2}$$

I don't get the first step

Answer 1

They use $(fg)'=f'g+g'f$. In this case $f=y(t)$ and $g=4+t^2$