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**vuze88** Suppose that f is a differentiable function of a single variable and $\displaystyle F(x,y)$ is defined by $\displaystyle F(x,y)=f(x^2-y)$.

Show that $\displaystyle F$ satisfies the partial differential equation $\displaystyle \frac{\partial F}{\partial x}+2x\frac{\partial F}{\partial y}=0$.

Given that $\displaystyle F(0,y)=\sin y$ for all $\displaystyle y$, find a formula for $\displaystyle F(x,y)$.

I'm pretty sure im supposed to use the chain rule for this but i dont know how to apply it. Can someone care to explain?