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Math Help - integrating factor

  1. #1
    Member i_zz_y_ill's Avatar
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    integrating factor

    I can't find an easy way to use the integrating factor to solve this question, any ideas?
    \frac{dy}{dx}+x^3y=0 The i.f is obviously exp{(x^4)/4} but I don't know where to go from there. thanks
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  2. #2
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    Quote Originally Posted by i_zz_y_ill View Post
    I can't find an easy way to use the integrating factor to solve this question, any ideas?
    \frac{dy}{dx}+x^3y=0 The i.f is obviously exp{(x^4)/4} but I don't know where to go from there. thanks

    This is a separable ODE, there is no need for integrating factors.

     \frac{dy}{y} = - x^3 dx .
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  3. #3
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    Hello, i_zz_y_ill!

    If you found the integrating factor,
    . . the next few steps are part of the procedure.
    Exactly where is your difficulty?


    \frac{dy}{dx}+x^3y\:=\:0

    The I.F is obviously: . e^{\frac{1}{4}x^4}
    but I don't know where to go from there. . You don't?

    Multiply by the I.F. . e^{\frac{1}{4}x^4}\frac{dy}{dx} + x^3e^{\frac{1}{4}x^4} y \:=\:0


    We have: . \frac{d}{dx} \left(e^{\frac{1}{4}x^4}y\right) \;=\;0


    Integrate: . e^{\frac{1}{4}x^4}y \;=\;C


    Therefore: . y \;=\;Ce^{-\frac{1}{4}x^4}

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