# Math Help - Verify a solution

1. ## Verify a solution

Verify that $xy=lny +c$ is a solution of the differential equation $dy/dx=(y^2)/(1-xy)$ for every value of the constant c.

I can't figure this one out...I don't even know where to start. Some help would be much appreciated. Thanks!

2. Use implicit differentiation on $xy=\text{ln}y+c$.

3. Originally Posted by ChingKing08
Verify that $xy=lny +c$ is a solution of the differential equation $dy/dx=(y^2)/(1-xy)$ for every value of the constant c.

I can't figure this one out...I don't even know where to start. Some help would be much appreciated. Thanks!
we need to show that $xy=lny +c$ satisfy DE $dy/dx=(y^2)/(1-xy)$

start from $xy=lny +c$, differentiate it

$y + xy' = \frac{y'}{y}$

$y(y + xy') = y'$

$y^2 + xyy' = y'$

$y^2 = y'(1 - xy)$

$y' = \frac{y^2}{1-xy}$

so the equation $xy=\ln y +c$ satisfy the differential equation $dy/dx=(y^2)/(1-xy)$