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Math Help - 1st order differentiation

  1. #1
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    1st order differentiation

    dy/dx = x+y^2

    Do I use the intergrating factor and if so when I take y^2 to the other side to make it in the form p(x)y is the x just 1
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  2. #2
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    p(x)=-1
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  3. #3
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    Quote Originally Posted by cerium View Post
    dy/dx = x+y^2

    Do I use the intergrating factor and if so when I take y^2 to the other side to make it in the form p(x)y is the x just 1
    The DE is not linear so integrating factor cannot be used. I suggest you compare the form against other types of DE's you have been taught ....
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  4. #4
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    This is a non-trivial DE. Here is WolframAlpha's solution in terms of Bessel functions. My copy of Mathematica Version 4 yields a solution in terms of Airy functions. I should also point out that the substitution

    u=y-\dfrac{x^{2}}{2}

    changes the DE into the Ricatti equation

    u'=\dfrac{x^{4}}{4}+x^{2}u+u^{2}.

    You could do a series solution method.
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