If xdydx=y( y- x+1), the solution is:

Question

If $x\dfrac{dy}{dx}=y(\log y-\log x+1)$, the solution is:

Accepted Answer

With $y=vx$: $x\dfrac{dv}{dx}=v\ln v \implies \int\dfrac{dv}{v\ln v}=\int\dfrac{dx}{x} \implies \ln(\ln v)=\ln x+\ln c \implies \ln v=cx \implies \log(y/x)=cx$.

Solutions · 1