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Math Help - Diff eq

  1. #1
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    Diff eq

    for some reason i am having trouble doing this problem and i think it is really easy:

    dy/dx=x+3y


    I just don't see what to do can someone help me? thanks
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by jarny View Post
    for some reason i am having trouble doing this problem and i think it is really easy:

    dy/dx=x+3y


    I just don't see what to do can someone help me? thanks
    This is the same as \frac{\,dy}{\,dx}-3y=x

    This is a linear DE, and the integrating factor is \varrho\!\left(x\right)=e^{\int 3\,dx}=e^{3x}

    Thus, we now see that \frac{\,d}{\,dx}\left[ye^{3x}\right]=xe^{3x}.

    Now, integrating both sides yields ye^{3x}=\int xe^{3x}\,dx

    Can you continue on from here?
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