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 $$ \sqrt{4+y^2}=\frac{1}{2}\ln(9+x^2)+C. $$