ODE No. 1570

2.1570 ODE No. 1570

Problem in Latex
Mathematica input
Maple input

$y (x) ((a^{2} - c^{2} ν^{2}) (a^{2} + 4 a c - c^{2} ν^{2} + 4 c^{2}) - b^{4} c^{4} x^{4 c}) + x^{2} (2 a^{2} + 4 (a + c - 1)^{2} + 4 (a - 1) (c - 1) - 2 c^{2} ν^{2} - 1) y^{″} (x) + x (2 a + 2 c - 1) (- 2 a^{2} - (2 a - 1) (2 c - 1) + 2 c^{2} ν^{2}) y^{'} (x) + x^{3} (- 4 a - 4 c + 6) y^{(3)} (x) + x^{4} y^{(4)} (x) = 0$ ✓ Mathematica : cpu = 0.0982249 (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 = 0.114 (sec), leaf count = 49

${y (x) = x^{a} (Y_{ν} (i b x^{c})_C 4 + Y_{ν} (x^{c} b)_C 2 + J_{ν} (i b x^{c})_C 3 + J_{ν} (x^{c} b)_C 1)}$

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