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Math Help - integrating factor Solve x(dy/dx)=y+x^3

  1. #1
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    integrating factor Solve x(dy/dx)=y+x^3

    Solve x(dy/dx)=y+x^3

    when y=3 and x =1





    have i done this correct ?
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  2. #2
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    Re: integrating factor Solve x(dy/dx)=y+x^3

    It all looks good until you say \displaystyle \int P ~dx = -\frac{1}{x} = \ln x which makes little sense.

    You are trying to find an integrating factor \displaystyle I = e^{\int -\frac{1}{x}~dx} go from there.
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    Re: integrating factor Solve x(dy/dx)=y+x^3

    Quote Originally Posted by pickslides View Post
    It all looks good until you say \displaystyle \int P ~dx = -\frac{1}{x} = \ln x which makes little sense.

    You are trying to find an integrating factor \displaystyle I = e^{\int -\frac{1}{x}~dx} go from there.
    As pickslides said, you were good until the middle term of this compound equation: \displaystyle \int P ~dx = -\frac{1}{x} = \ln x\,.

    It should have been: \displaystyle \int P ~dx = \int-\frac{1}{x} \,dx= -\ln x\,. We ignore the integration constant when finding an integrating factor.

    The integrating factor is then: e^{-ln(x)}\,, which can be simplified.
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