# Thread: sketch an approximate solution curve through each of the points...

1. ## sketch an approximate solution curve through each of the points...

by hand sketch an approximate solution curve through each of the points.

ok so the function is:

y(dy/dx) = -x so, (dy/dx) = -x/y at the point y(1)= 1 and y(0) = 4

so at the point 1,1 the slope is -1, so my dash is going up and to the left? is this all im doing with this problem or am i missing something?

2. It's well known that circles have a derivative of $\displaystyle \displaystyle -\frac{x}{y}$.

You can check this by solving the DE...

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

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

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

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

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

$\displaystyle \displaystyle x^2 + y^2 = r^2$ where $\displaystyle \displaystyle r^2 = 2(C_1 - C_2)$.

Now you can use your boundary conditions to evaluate $\displaystyle \displaystyle r^2$.