This question has stumped me too,
I need to find the general solution in implicit form of,
dy/dx = sqrt (10+y^2) / y
(x>0, y>o)
If it's $\displaystyle \frac{dy}{dx}=\frac{\sqrt{10+y^2}}{y}$ then just separate variables and integrate both sides:
$\displaystyle \int \frac{y dy}{\sqrt{10+y^2}}=\int dx$
I get $\displaystyle (x+c)^2-y^2=10$.