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Math Help - For which values of m does x^m satisfy the D.E.? Just wanting a double check.

  1. #1
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    For which values of m does x^m satisfy the D.E.? Just wanting a double check.

    Since I kept getting this wrong last night I thought I should double check with ya'll to make sure I'm doing everything correctly. Thanks.

    For which values of m, does x^m satisfy the following D.E.? 3x^2(\frac{d^2y}{dx^2}) + 11x(\frac{dy}{dx})-3y=0

    So my strategy is to just substitute x^m for y and find the values of m such that the equation equals 0.
    y=x^m
    y'=mx^{m-1}
    y''=m(m-1)x^{m-2}

    After substituting;

    3x^2(m(m-1)x^{m-2}) + 11x(mx^{m-1})-3(x^m)=0

    there's a cancellation in the first two terms, since x^{m-2}=\frac{x^m}{x^2}

    3(m(m-1)x^{m} +11mx^m -3x^m=0

    x^m(3m^2-3m+11m-3)=0

    so the discriminant is b^2-4ac=8^2-4*3*-3=100

    (-8+10)/2*3=1/3 and (-8-10)/2*3=-3
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  2. #2
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    Re: For which values of m does x^m satisfy the D.E.? Just wanting a double check.

    Yes, m= 1/3 and m= -3 are correct.
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