If $\displaystyle x^2y = (x+y)^3$
show that dy/dx = y/x
HOW??????
Thanks
Differentiating implicitly:
$\displaystyle 2xydx+x^2dy=3(x+y)^2dx+3(x+y)^2dy\Longrightarrow(x ^2-3(x+y)^2)dy=(3(x+y)^2-2xy)dx$ $\displaystyle \Longrightarrow -(2x^2+6xy+3y^2)dy=(3x^2+4xy+3y^2)dx\Longrightarrow$
$\displaystyle \frac{dy}{dx}=-\frac{3x^2+4xy+3y^2}{2x^2+6xy+3y^2}\neq \frac{y}{x}$ ...and thus the claim seems to be false.
Tonio