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

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


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 $Y=VX$

  • $\begingroup$ Thanks a lot sir, was it that easy.. :( I didn't even noticed it. $\endgroup$ – Adarsh Oct 9 '14 at 11:52
  • $\begingroup$ we're always learning to notice things - part of the fun! $\endgroup$ – David Holden Oct 9 '14 at 12:03

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