1 Differentiation
Find the solution of $$\displaystyle \frac{x+y\frac{dy}{dx}}{y-x\frac{dy}{dx}}=x^{2}+2y^{2}+\frac{y^{4}}{x^{2}}$$
1) $$\displaystyle \frac{x}{y}-\frac{1}{2\left ( x^{2}-y^{2} \right )}=c$$ 2) $$\displaystyle \frac{y}{x}+\frac{1}{2\left ( x^{2}+y^{2} \right )}=c$$ 3) $$\displaystyle \frac{x}{y}-\frac{1}{2\left ( x^{2}+y^{2} \right )}=c$$ 4) $$\displaystyle \frac{y}{x}-\frac{1}{2\left ( x^{2}+y^{2} \right )}=c$$ .
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