Hint on How to solve this differential equation?

Question

I have the differential equation

$$v’(x)=(x-v(x))\cdot g(x)$$

For some function $g(x)$. Can you give a hint on how to solve this?

Answer 1

Make a substitution $x-v(x) = z(x)$

Then $1-v'(x) = z(x)'$

$1-z(x)'=z(x)*g(x)$

$z(x)'+z(x)*g(x)=1$

This is linear first order nonhomogenous equation, I think you shouldn't have problems with it