If the general solution of y'=yx+(xy) is y|cx|=x (c arbitrary), then (2) is:

Question

If the general solution of $y'=\dfrac{y}{x}+\phi\left(\dfrac{x}{y}\right)$ is $y\ln|cx|=x$ ($c$ arbitrary), then $\phi(2)$ is:

Accepted Answer

With $y=vx$ and differentiating the given general solution, matching forms gives $\phi(1/v)=-1/v^2$, so at $x/y=2$: $\phi(2)=-1/4$.

Solutions · 1