Math Help - First Order Diffy Q

1. First Order Diffy Q

Sorry I'm not good with the latex stuff yet, but can someone please solve this equation:

(2x+4y-2)dx + (-3x-2y+1)dy=0

2. Originally Posted by Jake8054
Sorry I'm not good with the latex stuff yet, but can someone please solve this equation:

(2x+4y-2)dx + (-3x-2y+1)dy=0
Introduce new variables $(r,s)$ as to eliminate the $-2$ and $1$ in your equation. So if $x = r + a$ and $y = s + b$ ( $a$ and $b$ to be determined) then

$
\left(2(r+a) + 4(s+b) - 2 \right)\,dr + \left(-3(r+a) - 2(s+b) + 1 \right)\,ds =0
$

This means solving

$
\begin{array}{c}
2a + 4b = 2,\\
-3a -2b = -1
\end{array}$

Then your ODE becomes

$
\left(2r + 4s \right)\,dr + \left(-3 r - 2 s \right)\,ds =0
$

which is homogeneous.