Reducing differential equation $\frac{\operatorname d \!y}{\operatorname d \!x} = \frac{(x+y)^2 }{(x+2)(y-2)}$

Question

I'm not able to reduce the following differential equation to variable seperable form. Tried a lot. Please guide..

$$\dfrac{\operatorname d \!y}{\operatorname d \!x} = \dfrac{(x+y)^2 }{(x+2)(y-2)}$$

Answer 1

set $X=x+2$ and $Y=y-2$ so the equation becomes $$ \frac{dY}{dX}= \frac{(X+Y)^2}{XY} $$ you can now proceed using the standard substitution $Y=VX$