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Math Help - First Order Diffy Q

  1. #1
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    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
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  2. #2
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    Quote Originally Posted by Jake8054 View Post
    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

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

    This means solving

     <br />
\begin{array}{c}<br />
2a + 4b = 2,\\<br />
-3a -2b = -1<br />
\end{array}

    Then your ODE becomes

     <br />
\left(2r + 4s \right)\,dr + \left(-3 r - 2 s \right)\,ds =0<br />

    which is homogeneous.
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