I do not have an idea where to start to solve the following differential equation, so every tip is welcome.
$y' = \frac{x\sqrt{4+y^{2}}}{y(9+x^{2})} $
I do not have an idea where to start to solve the following differential equation, so every tip is welcome.
$y' = \frac{x\sqrt{4+y^{2}}}{y(9+x^{2})} $
We write your equation as $ \frac{y}{\sqrt{4+y^2}}dy=\frac{x}{9+x^2}dx $ or equivalenlently, $ d(\sqrt{4+y^2})=d((1/2)\ln(9+x^2)). $ Hence, we get $ \sqrt{4+y^2}=\frac{1}{2}\ln(9+x^2)+C. $