Math Help - Existence and Uniqueness Th.

1. Existence and Uniqueness Th.

Discuss the application of the existence and uniqueness theorem to the initial value problem

y' = (x - y)/(x + 3y) ; y(0) = -1

2. The equation is written in 'normal fashion'...

$y^{'}= f(x,y)$ , $y(x_{0})=y_{0}$ (1)

... where...

$f(x,y)= \frac{x-y}{x+3\cdot y}$ , $x_{0}=0$ , $y_{0}= -1$

The partial derivative of $f(*,*)$ respect to y is...

$f_{y}^{'}= - \frac {4\cdot x}{(x+3y)^{2}}$

Both $f(*,*)$ and $f_{y}^{'}(*,*)$ are continous in $[0,1]$ so that does exist one and only one solution of (1) crossing that point...

Kind regards

$\chi$ $\sigma$

3. My first thought would be "What IS the existence and uniqueness theorem?" What exactly does it say?