# Thread: determine a region in the xy plane...

1. ## determine a region in the xy plane...

ok so im supposed to determine a region in the xy plane that would have a unique solution whose graph passes through a point in the region. (x+3y)y' = 2x - y

im not sure where to start this problem. am i supposed to find a point that satisfies the equation? any help would be appreciated.

thanks

2. Maybe you should solve the differential equation at the beginning??

3. Originally Posted by slapmaxwell1
ok so im supposed to determine a region in the xy plane that would have a unique solution whose graph passes through a point in the region. (x+3y)y' = 2x - y

Consider the domain:

$D=\left\{{(x,y)\in \mathbb{R}^2:x+3y\neq 0}\right\}$

and

$y'=f(x,y)=\dfrac{2x-y}{x+3y}$

We have:

$(i)\quad f\rightarrow{\mathbb{R}}" alt="(i)\quad f\rightarrow{\mathbb{R}}" /> is continuous.

$(ii)\quad \dfrac{{\partial f}}{{\partial y}}\in\mathcal{C}^1(D)$

Now, use a well known existence and uniqueness theorem.

Fernando Revilla

4. thanks fernando. i went back and redid the problem. and yes i looked at where the domain would not exist and used that to help me to find my domain.