Determine for which values of m the functions phix xm is a

Determine for which values of m the functions phi(x) = x^m is a solution to the equation 3x^2 d^2y/dx^2 + 11xdy/dx - 3y = 0.

y =x^m

y\'= mx^(m-1)

y\'\'=m(m-1)x^(m-2)

3x^2 y\'\' + 11xy\' -3y=0

3x^2(m)(m-1)x^(m-2) + 11xmx^(m-1) - 3x^m=0

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

taking out x^m

3m(m-1)+11m-3=0

3m^2-3m+11m-3=0

3m^2+8m-3=0

3m^2+9m-m-3=0

3m(m+3)-1(m+3)=0

(3m-1)(m+3)=0

m=1/5,-3

$Determine for which values of m the functions phi(x) = x^m is a solution to the equation 3x^2 d^2y/dx^2 + 11xdy/dx - 3y = 0. Solutiony =x^m y\'= mx^(m-1) y\'\'$

Determine for which values of m the functions phix xm is a

Solution

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