A curve which passes through the point (1,0) satisfies the equation dx/dy = x³

Find its equation

thanks for any help

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- Nov 16th 2008, 10:27 PMgraceyEquation
A curve which passes through the point (1,0) satisfies the equation dx/dy = x³

Find its equation

thanks for any help - Nov 16th 2008, 10:42 PMSoroban
Hello, gracey!

Quote:

A curve which passes through the point (1,0)

satisfies the equation: .$\displaystyle \frac{dx}{dy} \:=\:x^3$

Find its equation

We have: .$\displaystyle \frac{dy}{dx} \:=\:x^{-3} \quad\Rightarrow\quad dy \:=\:x^{-3}\,dx$

Integrate: .$\displaystyle \int dy \;=\;\int x^{-3}\,dx \quad\Rightarrow\quad y \;=\;-\frac{x^{-2}}{2} + C \;=\;-\frac{1}{2x^2} + C$

Since (1,0) satisfies the equation: .$\displaystyle 0 \:=\:-\frac{1}{2\cdot1^2} + C \quad\Rightarrow\quad C \:=\:\frac{1}{2}$

Therefore, the equation is: .$\displaystyle y \;=\;-\frac{1}{2x^2} + \frac{1}{2}$

- Nov 16th 2008, 10:42 PMmr fantastic