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Math Help - to be exact or not exact? this is the question...

  1. #1
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    to be exact or not exact? this is the question...

    ok so i have this problem, and im having a little trouble separating it..here is the function:

    x(dy/dx) = 2xe^x - y + 6x^2

    i cant get this problem separated so that i can solve it for exactness. because there is only one y, i guess i want the My=0 and Nx=0. any thoughts? thanks in advance...
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  2. #2
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    Remember, the standard form for exact equations is

    M(x,y)dx + N(x,y)dy = 0, where you need M_y = N_x.

    For you,

    x dy = \left(2x e^x + 6x^2 - y\right)dx

    so

     \left(2x e^x + 6x^2 - y\right)dx - x dy = 0.
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  3. #3
    Member Miss's Avatar
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    Another way:

    \left(2x e^x + 6x^2 - y\right)dx - x dy = 0
    \implies (2xe^x+6x^2)dx-(ydx+xdy)=0
    \implies (2xe^x+6x^2)dx-d(xy)=0

    Now, just integrate.
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