Solve this


Find $\frac{\mathrm{dy}}{\mathrm{dx}}$ in each of the following:

$(x+y)^{2}=2 a x y$


We are given with an equation $(x+y)^{2}=2 a x y$, we have to find $\frac{d y}{d x}$ of it, so by differentiating the equation on both sides with respect to $x$, we get,

$2(x+y)\left(1+\frac{d y}{d x}\right)=2 a\left[y+x \frac{d y}{d x}\right]$

$x+y+\frac{d y}{d x}[x+y]=a\left[y+x \frac{d y}{d x}\right]$

$\frac{d y}{d x}[x+y-a x]=a y-x-y$

$\frac{d y}{d x}=\frac{y(a-1)-x}{y+x(1-a)}$

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