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... 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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1 Answer 1

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.

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I got (-1/9)y^(-9)=(-1/2)x^(-2)+C –  Ryan Oct 4 '12 at 22:25
But it's not right. –  Ryan Oct 4 '12 at 22:26
NVM got it. Thanks! –  Ryan Oct 4 '12 at 22:28
You need to evaluate $C$ using the initial condition. –  André Nicolas Oct 4 '12 at 22:29

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