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Math Help - Linear Equartions!

  1. #1
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    Linear Equartions!

    I am having trouble with this problem:

    x^2y'-4xy=x^7e^{x^2}+3x^5

    First step I divided by  x^2 then I find that p(x)= -4/x and q(x)= x^5e{x^2}+3x^2. I that right? Well, if that is right, I am stuck at that point.
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  2. #2
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    Works for me.
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  3. #3
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    Can you help from that point? How do I simplify the right side which is a mess?
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  4. #4
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    You need to solve for the integrating factor.

    y*e^{\int p(x)dx}=\int q(x)e^{\int p(x)dx}dx
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  5. #5
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    Yes I know but I haven't yet integrated the right side which is the G'(x) because I don't know how to start there.
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  6. #6
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    e^{4\int \frac{1}{x}dx}=x^4

    y x^4= \int x^4(x^7e^{x^2}+3x^5)dx

    Break into 2 seperate integrals. For the first, integration by parts and the second is just straight forward. Lastly, divide by x^4
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