# Equation

• Nov 16th 2008, 10:27 PM
gracey
Equation
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 PM
Soroban
Hello, gracey!

Quote:

A curve which passes through the point (1,0)
satisfies the equation: .$\displaystyle \frac{dx}{dy} \:=\:x^3$
Find its equation

This is a Differential Equation problem . . .

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 PM
mr fantastic
Quote:

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

Find its equation

thanks for any help

$\displaystyle \frac{dy}{dx} = x^{-3}$.

Integrate to get y as a function of x. Use "curve which passes through the point (1,0)" to evaluate the constant of integration.