ODE No. 1491

5.43 ODE No. 1491

$x^{2} \frac{d^{3}}{d x^{3}} y (x) + 3 x \frac{d^{2}}{d x^{2}} y (x) + (4 a^{2} x^{2 a} + 1 - 4 ν^{2} a^{2}) \frac{d}{d x} y (x) = 4 a^{3} x^{2 a - 1} y (x) = 0$

Problem in Latex
Mathematica input
Maple input

Mathematica: cpu = 0.046006 (sec), leaf count = 102 ${{y (x) \to c_{2} {(x^{2 a})}^{- ν}_{1} F_{2} (- ν - \frac{1}{2}; 1 - 2 ν, 1 - ν; - x^{2 a}) + c_{3} {(x^{2 a})}^{ν}_{1} F_{2} (ν - \frac{1}{2}; ν + 1, 2 ν + 1; - x^{2 a}) + c_{1}_{1} F_{2} (- \frac{1}{2}; 1 - ν, ν + 1; - x^{2 a})}}$

Maple: cpu = 0.063 (sec), leaf count = 88 ${y (x) =_C 1_{1} F_{2} (- \frac{1}{2}; ν + 1, - ν + 1; - x^{2 a}) +_C 2 x^{- 2 a ν}_{1} F_{2} (- \frac{1}{2} - ν; 1 - 2 ν, - ν + 1; - x^{2 a}) +_C 3 x^{2 a ν}_{1} F_{2} (ν - \frac{1}{2}; 2 ν + 1, ν + 1; - x^{2 a})}$

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