ODE No. 1325

4.325 ODE No. 1325

$\frac{d^{2}}{d x^{2}} y (x) = - \frac{((a + b + 1) x + α + β - 1) \frac{d}{d x} y (x)}{x (x - 1)} - \frac{(a b x - α β) y (x)}{x^{2} (x - 1)} = 0$

Problem in Latex
Mathematica input
Maple input

Mathematica: cpu = 0.264534 (sec), leaf count = 52 ${{y (x) \to (- 1)^{α} c_{1} x^{α}_{2} F_{1} (a + α, α + b; α - β + 1; x) + (- 1)^{β} c_{2} x^{β}_{2} F_{1} (a + β, b + β; - α + β + 1; x)}}$

Maple: cpu = 0.093 (sec), leaf count = 103 ${y (x) =_C 1 x^{α} {(x - 1)}^{1 - a - α - b - β}_{2} F_{1} (1 - b - β, 1 - a - β; 1 + α - β; x) +_C 2 x^{β} {(x - 1)}^{1 - a - α - b - β}_{2} F_{1} (1 - a - α, 1 - α - b; 1 - α + β; x)}$

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