Question Number 29324 by mondodotto@gmail.com last updated on 07/Feb/18
Answered by ajfour last updated on 07/Feb/18
![e^y ((dy/dx))=3x^2 +tan^(−1) y+((x/(1+y^2 )))(dy/dx) (dy/dx) = ((3x^2 +tan^(−1) y)/([e^y −(x/(1+y^2 ))])) .](https://www.tinkutara.com/question/Q29327.png)
$${e}^{{y}} \left(\frac{{dy}}{{dx}}\right)=\mathrm{3}{x}^{\mathrm{2}} +\mathrm{tan}^{−\mathrm{1}} {y}+\left(\frac{{x}}{\mathrm{1}+{y}^{\mathrm{2}} }\right)\frac{{dy}}{{dx}} \\ $$$$\frac{{dy}}{{dx}}\:=\:\frac{\mathrm{3}{x}^{\mathrm{2}} +\mathrm{tan}^{−\mathrm{1}} {y}}{\left[{e}^{{y}} −\frac{{x}}{\mathrm{1}+{y}^{\mathrm{2}} }\right]}\:\:. \\ $$