Question

Find $\frac{dy}{dx}$ of $xy+y^2=\tan x+y$

Answer 1

$xy+y^2=\tan x+y$
Differentiating both sides w.r.t $x$ we get,
$\Rightarrow y+x\frac{dy}{dx}+2y\frac{dy}{dx}={\sec }^{2}x+\frac{dy}{dx}$
$\Rightarrow \frac{dy}{dx}=\frac{{\sec }^{2}x-y}{x+2y-1}$