please help!!!! ---differential equations:

x'=3x-2y
and
y'=2x-2y

Question

please help!!!! ---differential equations:

x'=3x-2y
and
y'=2x-2y

anonymous · Answer

Ok, and then what?

anonymous · Answer

solving simultaneously

anonymous · Answer

For x and y?

Is x' = dx/dy and y' = dy/dx?

anonymous · Answer

yes... that's correct

anonymous · Answer

Hmm, I can see how to get an equation in x and y from that, but do you want numerical values for both x and y?

I'll have to look at this a different way. Just a sec.

anonymous · Answer

The first thing I thought of was that x' and y' are reciprocals, so you could do
$\large 3x-2y=(2x-2y)^{-1}$ and rearrange from there...

anonymous · Answer

still confused...

anonymous · Answer

Me too. I'm not sure exactly what you're looking for.

anonymous · Answer

Is there any other information or detail in the question for what the answer should look like?

anonymous · Answer

an example in class, she said solve one eqn... let's say y=.. differentiate it and substitute in eqn (2)

anonymous · Answer

Ok, that sounds reasonable, being standard system solving procedure.

That would look like this:

$\large x'=3x-2y \rightarrow y=(-1/2)(x'-3x)$

$\large y'=2x-2y \rightarrow x=(1/2)(y'+2y)$

Differentiating x:

$\large x'=(1/2)(y''+2)$

Sub into other equation:

$\large  y=(-1/2)((1/2)(y''+2)-3(1/2)(y'+2y))$

Simplify and rearange into a second-order DE.

$\large $