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Math Help - finidng the general solution

  1. #1
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    Exclamation finidng the general solution

    Find the general solution of the equation:

    1= [3y*cos(y^2)*dy/dx] + [3e^(-x) * ycos(y^2) * dy/dx]

    really really stuck on this, any help would be appreciated!
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  2. #2
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    Quote Originally Posted by bobguy View Post
    Find the general solution of the equation:

    1= [3y*cos(y^2)*dy/dx] + [3e^(-x) * ycos(y^2) * dy/dx]

    really really stuck on this, any help would be appreciated!
    If you factor the RHS you get

     <br />
1 = 3y \cos \left(y^2\right) \left(1 + e^{-x}\right) \frac{dy}{dx}<br />

    at which point we recognize this is separable, so

     <br />
\frac{dx}{1+e^{-x}} = 3y \cos \left(y^2\right)dy<br />

    or

     <br />
\frac{e^x\,dx}{e^{x}+1} = 3y \cos \left(y^2\right)dy<br />
.

    Now integrate each side.
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