$\displaystyle (2x^{2}-x)y''+(2x-2)y'+(-2x^{2}+3x-2)y=0$

Please help me to solve this one by "Frobenius Method"

Thanks

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- Jun 25th 2010, 12:14 PMsinichkoFrobenius Method
$\displaystyle (2x^{2}-x)y''+(2x-2)y'+(-2x^{2}+3x-2)y=0$

Please help me to solve this one by "Frobenius Method"

Thanks - Jun 25th 2010, 12:30 PMAckbeet
What steps have you taken so far?

- Jun 26th 2010, 02:51 PMHallsofIvy
Around what value of x? Since $\displaystyle 2x^2- x= x(2x- 1)= 0$ only for x= 0 or x= 1/2, "Frobenius' method" only applies to solutions as power series about 0 or 1/2.

Start by writing $\displaystyle y= \sum_{n=0}^\infty a_n(x- x_0)^{n+c}$ where $\displaystyle x_0$ is either 0 or 1/2.