83: Frobenius method will be used to find a series solution of the following ODE near...

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83: Frobenius method will be used to find a series solution of the following ODE near the refular singular point Xo=0 Assuming a solution of the form y= C₁ (x-xo) ^ and substituting y, y' and y" înto the given ODE; n=0 a) find the indicial equation associated with the regular singular point Xo =0 and the roots r₁ and 12 of the indical equation (where Relry) = Re (₂)). Give all the details b) find the first 4 nonzero terms of the linearly independent solution associated with r=r₁. Give all the details. 11 3x²y" -4xy' + (x+2)y=0 2) 5x²y" - 4xy' + (x-2)y=0 3)3x²y" +xy' +(x-1)y=0 4)5x²y + 3xy +(x-3) y =0 513x²y-2xy + (x-2)y=0 83: Frobenius method will be used to find a series solution of the following ODE near the refular singular point Xo=0 Assuming a solution of the form y= C₁ (x-xo) ^ and substituting y, y' and y" înto the given ODE; n=0 a) find the indicial equation associated with the regular singular point Xo =0 and the roots r₁ and 12 of the indical equation (where Relry) = Re (₂)). Give all the details b) find the first 4 nonzero terms of the linearly independent solution associated with r=r₁. Give all the details. 11 3x²y" -4xy' + (x+2)y=0 2) 5x²y" - 4xy' + (x-2)y=0 3)3x²y" +xy' +(x-1)y=0 4)5x²y + 3xy +(x-3) y =0 513x²y-2xy + (x-2)y=0