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Math Help - [Derivatives] Finding the solution

  1. #1
    Junior Member Cthul's Avatar
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    [Derivatives] Finding the solution

    y=ax^2+bx

    Find the solution for the constants a & b.

    \frac{d^2y}{dx^2}+6\frac{dy}{dx}+36x=0

    I got as far as:

    y'=2ax+b
    y''=2a

    And don't know what to do next.
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  2. #2
    Member sbhatnagar's Avatar
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    Re: [Derivatives] Finding the solution

    Are you really sure that this is a derivative question?
    Is y a function of x?
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  3. #3
    Junior Member Cthul's Avatar
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    Re: [Derivatives] Finding the solution

    I think it might be a mistake or I'm supposed to solve for x. I still don't get the answer.
    Apparently a=-3 and b=1
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  4. #4
    Member sbhatnagar's Avatar
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    Re: [Derivatives] Finding the solution

    If you were supposed to solve for x then x=\frac{-b \pm \sqrt{b^2+4ay}}{2a} (using quadratic formula), else the question doesn't make any sense.

    If you were supposed to find a and b ,there would be 2 equations.
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  5. #5
    Junior Member Cthul's Avatar
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    Re: [Derivatives] Finding the solution

    Ah, thanks.
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  6. #6
    Member sbhatnagar's Avatar
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    Re: [Derivatives] Finding the solution

    ... also we can differentiate both L.H.S and R.H.S if and only if y is a function of x.
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  7. #7
    A Plied Mathematician
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    Re: [Derivatives] Finding the solution

    Quote Originally Posted by Cthul View Post
    y=ax^2+bx

    Find the solution for the constants a & b.

    \frac{d^2y}{dx^2}+6\frac{dy}{dx}+36x=0

    I got as far as:

    y'=2ax+b
    y''=2a

    And don't know what to do next.
    Plug the original function into the differential equation. Then equate like powers of x.
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