ODE No. 1570

6.37 ODE No. 1570

$x^{4} d 4 y (x) + (6 - 4 a - 4 c) x^{3} \frac{d^{3}}{d x^{3}} y (x) + (- 2 ν^{2} c^{2} + 2 a^{2} + 4 {(a + c - 1)}^{2} + 4 (a - 1) (c - 1) - 1) x^{2} \frac{d^{2}}{d x^{2}} y (x) + (2 ν^{2} c^{2} - 2 a^{2} - (2 a - 1) (2 c - 1)) (2 a + 2 c - 1) x \frac{d}{d x} y (x) + ((- ν^{2} c^{2} + a^{2}) (- ν^{2} c^{2} + a^{2} + 4 a c + 4 c^{2}) - b^{4} c^{4} x^{4 c}) y (x) = 0$

Mathematica: cpu = 0.154020 (sec), leaf count = 470 ${{y (x) \to c_{1} Γ (1 - ν) (- 1)^{\frac{a - c ν}{4 c}} 2^{- \frac{2 (a - c ν)}{c} - ν - 1} b^{\frac{a - c ν}{c} + ν} {(x^{4 c})}^{\frac{a - c ν}{4 c} + \frac{ν}{4}} (J_{- ν} (b \sqrt[4]{x^{4 c}}) + I_{- ν} (b \sqrt[4]{x^{4 c}})) + c_{2} Γ (2 - ν) (- 1)^{\frac{a - c ν + 2 c}{4 c}} 2^{- \frac{2 (a - c ν + 2 c)}{c} - ν + 1} b^{\frac{a - c ν + 2 c}{c} + ν - 2} {(x^{4 c})}^{\frac{a - c ν + 2 c}{4 c} + \frac{ν - 2}{4}} (I_{- ν} (b \sqrt[4]{x^{4 c}}) - J_{- ν} (b \sqrt[4]{x^{4 c}})) + c_{3} Γ (ν + 1) (- 1)^{\frac{a + c ν}{4 c}} 2^{- \frac{2 (a + c ν)}{c} + ν - 1} b^{\frac{a + c ν}{c} - ν} {(x^{4 c})}^{\frac{a + c ν}{4 c} - \frac{ν}{4}} (J_{ν} (b \sqrt[4]{x^{4 c}}) + I_{ν} (b \sqrt[4]{x^{4 c}})) + c_{4} Γ (ν + 2) (- 1)^{\frac{a + c ν + 2 c}{4 c}} 2^{- \frac{2 (a + c ν + 2 c)}{c} + ν + 1} b^{\frac{a + c ν + 2 c}{c} - ν - 2} {(x^{4 c})}^{\frac{a + c ν + 2 c}{4 c} + \frac{1}{4} (- ν - 2)} (I_{ν} (b \sqrt[4]{x^{4 c}}) - J_{ν} (b \sqrt[4]{x^{4 c}}))}}$

Maple: cpu = 0.047 (sec), leaf count = 57 ${y (x) =_C 1 x^{a} J_{ν} (x^{c} b) +_C 2 x^{a} Y_{ν} (x^{c} b) +_C 3 x^{a} J_{ν} (i b x^{c}) +_C 4 x^{a} Y_{ν} (i b x^{c})}$

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