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

I've gotten to this so far, but I've no clue if it's right.

Answer 2

\[
y(x)=\frac{x}{c+x}\\
y'(x)=\frac{c}{(c+x)^2}\\
\frac{y(x)-y(x)^2}{x}=\frac{\frac{x}{c+x}-\frac{x^2}{(c+x)^2}}{x
}=\frac{c}{(c+x)^2}=y'(x)
\]

Answer 3

Thank you, I think I've got it now.

Answer 4

You also can solve it directly. It is a separable differential equation.