Question

Prove that y = x/(x+c) is a general solution for the differntial equation dy/dx = (y - y^2)/x and show that all solutions contain (0,0).

Answer 1

So far, I've gotten:
\[\frac{ dy }{ dx } = \frac{ y-y ^{2} }{ x } \]
\[y = \frac{( x(\frac{ dy }{ dx }) - y ) - (x2y(\frac{ dy }{ dx }) - y^{2})}{ x^{2} } \]
\[y = \frac{ 2y(y-y^{2}) - (y-y^{2}) }{ x^{2} }\]