1. anonymous

$xy.\frac{dy}{dx}=1-x^2$This is again separable. Divide both sides by x and 'multiply' both sides by dx to get$y.dy=\frac{1-x^2}{x}dx=(\frac{1}{x}-x)dx$Integrate both sides:$\frac{y^2}{2}=\ln(x)-\frac{x^2}{2}+c_1 \rightarrow y^2=2\ln(x)-x^2+c_2$where c_1 and c_2 are just constants.

2. anonymous

thank u very much, sir

3. anonymous

You're welcome.