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Math Help - find the general solution

  1. #1
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    find the general solution

    I was told to find the general solution to this problem:



    I rearranged it to put it in standard form and got:

    dy/dx + 2x^4 (y) = -x^5 +x^2 + 4x -3

    then, finding mu(x) = e^(intergral of (2x^4)dx)

    multiplying both sides by mu(x), then solving for y(x), I eventually got:

    y(x) = (1/5)(1/e^((2x^5)/5)) * [intergral of (mu(x) * (-x^5 +x^2 + 4x - 3)dx]

    this is about where I get stuck. This intergral is a monster!!!

    I've tried multiplying through, then doing each individual intergral, but... its still aweful. Am I doing something wrong?
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  2. #2
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    Quote Originally Posted by fruitbodywash View Post
    I was told to find the general solution to this problem:



    I rearranged it to put it in standard form and got:

    dy/dx + 2x^4 (y) = -x^5 +x^2 + 4x -3

    then, finding mu(x) = e^(intergral of (2x^4)dx)

    multiplying both sides by mu(x), then solving for y(x), I eventually got:

    y(x) = (1/5)(1/e^((2x^5)/5)) * [intergral of (mu(x) * (-x^5 +x^2 + 4x - 3)dx]

    this is about where I get stuck. This intergral is a monster!!!

    I've tried multiplying through, then doing each individual intergral, but... its still aweful. Am I doing something wrong?
    Dear fruitbodywash,

    How did you got, dy/dx + 2x^4 (y) = -x^5 +x^2 + 4x -3 I think there is a mistake.

    But you could rearrange this as,

    (x^{5}+5)\frac{dy}{dx}=x^2+4x-3-10x^{4}y

    \frac{dy}{dx}+\left(\frac{10x^{4}}{x^{5}+5}\right)  y=x^{2}+4x-3

    This is a linear differential equation and could be solved using the method you have used.

    Hope this will help you.
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