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Math Help - Second Order Differential Equation

  1. #1
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    Second Order Differential Equation

    Determine the values of a, b and c given that y=ax^2+bx+c is a solution to x^2(y'')^2+y^2=80x^4+72x^3+50x^2+24x+16 given the values a,  b and c are positive.

    y'=2ax+b and y''=2a hence a^2x^4+2abx^3+(2ac+b^s+4a^2)x^2+c^2=80x^4+72x^3+50  x^2+24x+16

    However, from these results, I am not sure exactly how to determine which values you would use. I figured a=\sqrt{80} and c=4, however, you get more than one option for b. Any help is greatly appreciated!
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  2. #2
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    Re: Second Order Differential Equation

    Why do you believe there has to only be one value for b?
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    Re: Second Order Differential Equation

    Well, the answer depends on only one value for B.
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    Re: Second Order Differential Equation

    I am supposed to give the result of sin(A)+sin(2B)+sin(3C); if I have more than one answer for B, that proves to be a bit difficult.
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