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Math Help - plz assist me...

  1. #1
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    plz assist me...

    Q: solve diff equation:
    [2ysin(x)+3y^4*sin(x)cos(x)]dx-[4y^3*cos^2(x)+cos(x)]dy=0
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  2. #2
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    Quote Originally Posted by Mathventure View Post
    Q: solve diff equation:
    [2ysin(x)+3y^4*sin(x)cos(x)]dx-[4y^3*cos^2(x)+cos(x)]dy=0
    If you multiply by \cos x the equation becomes exact.
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  3. #3
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    Quote Originally Posted by danny arrigo View Post
    If you multiply by \cos x the equation becomes exact.
    but what is method to calculate integrating factor cos(x)??
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  4. #4
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    Quote Originally Posted by Mathventure View Post
    but what is method to calculate integrating factor cos(x)??
    IF your ODE M dx + N dy = 0 is not exact ie. M_y = N_x then one looks for an integrating factor \mu such that

    \left(\mu M\right)_y = \left( \mu N \right)_x

    If \mu = \mu(x) only then

    \frac{\mu_x}{\mu} = \frac{M_y-N_x}{N} which in your case it is (very fortunate)!
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