# sketch an approximation solution

• Jan 29th 2011, 11:06 PM
slapmaxwell1
sketch an approximation solution
ok so y(dy/dx) = -x y(0) = 0 and im supposed to draw an approximation solution curve going through the point ? im not sure what i should be doing here. so i separated the variables and got y= sqrt(-x^2 + C). which i dont think can be sketch because its negative under the radical sign. any help would be appreciated
• Jan 29th 2011, 11:18 PM
Prove It
$\displaystyle y\,\frac{dy}{dx} = -x$

$\displaystyle \int{y\,\frac{dy}{dx}\,dx} = \int{-x\,dx}$

$\displaystyle \int{y\,dy} = -\frac{x^2}{2} + C_1$

$\displaystyle \frac{y^2}{2}+C_2 = -\frac{x^2}{2} + C_1$

$\displaystyle \frac{y^2}{2} = -\frac{x^2}{2} + C_1 - C_2$

$\displaystyle y^2 = -x^2 + C$ where $\displaystyle C = 2C_1 - 2C_2$

$\displaystyle x^2 + y^2 = C$.

Once you use your initial condition to find $\displaystyle C = 0$, you'll see that this is a circle of radius $\displaystyle 0$, in other words, the only point is the origin.
• Jan 30th 2011, 01:53 AM
slapmaxwell1
thanks. let me go back and re work it.