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Math Help - First Order Linear Differential Equation

  1. #1
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    First Order Linear Differential Equation

    I was having a problem trying to identify the P(x) and q(x) of this question,

    (X^3)d/dx(y(x))-(4X^2)y(x)=(4x^7)

    I would be really thankful if someone could help me with this!

    Thanks!
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by anthony162 View Post
    (X^3)d/dx(y(x))-(4X^2)y(x)=(4x^7)

    Dividing x^3y'-4x^2y=4x^7 by x^3 we get y'-(4/x)y=4x^4 .


    So, p(x)=-4/x,\;q(x)=4x^4 .
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  3. #3
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    Thanks alot i've just found out that i had mistaken that the y(x) is part of another equation,thanks for your help!
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  4. #4
    MHF Contributor FernandoRevilla's Avatar
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    All right, take into account that


    \dfrac{d}{dx}\;(y(x)):=y'(x)
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  5. #5
    A Plied Mathematician
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    The equation is also Cauchy-Euler.
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