The solution curve of ydxdy=x(_ex-_ey+1), x0,y0, passing through (e,1), is:

Question

The solution curve of $y\dfrac{dx}{dy}=x(\log_ex-\log_ey+1)$, $x>0,y>0$, passing through $(e,1)$, is:

Accepted Answer

With $y=vx$: $\dfrac{dx}{x}$ relation gives, after simplification, $\ln\left|\dfrac{x}{y}\right|=y+C$; using $(e,1)$: $C=0$, so $\log_e|x/y|=y$.

Solutions · 1