# Find the equation of curve through $(1,1)$ the slope of whose tangent line at $(x,y)$ is $y^{10}/x^3$

... Express you answer as y^-9 =

I assume I need to set up a differential equation, but I do not even know where to begin.

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Solve the differential equation $$\frac{dy}{dx}=\frac{y^{10}}{x^3}$$ with initial condition $y(1)=1$. The variables can be separated, so solving the DE should not be difficult.
Why? Because the differential equation above says exactly that the slope of the tangent line at $(x,y)$, which is $\dfrac{dy}{dx}$, is equal to the expression on the right.
You need to evaluate $C$ using the initial condition. –  André Nicolas Oct 4 '12 at 22:29