Question

How to find the general solution of `x dy/dx = xy + y` ?

Answer 1

`y = Axe^x`, where `A` is a constant.

Explanation:

We do a little bit of algebra before integrating to separate the variables:

`x(dy/dx) = y(x +1)`

`dy/(y dx) = (x +1)/x`

`(dy)/y = (x + 1)/x dx`

`lny = int 1 + 1/xdx`

`lny = x + lnx + C`

`y = Ae^(x + lnx)`

`y = Ae^xe^(lnx)`

`y = Axe^x`

Hopefully this helps!