ODE No. 1434

4.434 ODE No. 1434

$\frac{d^{2}}{d x^{2}} y (x) = - \frac{b \cos (x) \frac{d}{d x} y (x)}{\sin (x) a} - \frac{(c {(\cos (x))}^{2} + d \cos (x) + e) y (x)}{a {(\sin (x))}^{2}} = 0$

Mathematica: cpu = 99.286108 (sec), leaf count = 1596424

Result too large for latex to process

Maple: cpu = 0.936 (sec), leaf count = 559 ${y (x) =_C 1 {(\sin (x))}^{- \frac{a + b}{2 a}} {(\cos (x) + 1)}^{\frac{1}{4 a} (2 a + \sqrt{a^{2} + (- 2 b - 4 c - 4 d - 4 e) a + b^{2}})} {(- 1 + \cos (x))}^{- \frac{1}{4 a} (- 2 a + \sqrt{a^{2} + (- 2 b - 4 c + 4 d - 4 e) a + b^{2}})}_{2} F_{1} (\frac{1}{4 a} (\sqrt{a^{2} + (- 2 b - 4 c - 4 d - 4 e) a + b^{2}} + 2 1434 \sqrt{4 a c - b^{2}} - \sqrt{a^{2} + (- 2 b - 4 c + 4 d - 4 e) a + b^{2}} + 2 a), - \frac{1}{4 a} (2 1434 \sqrt{4 a c - b^{2}} + \sqrt{a^{2} + (- 2 b - 4 c + 4 d - 4 e) a + b^{2}} - \sqrt{a^{2} + (- 2 b - 4 c - 4 d - 4 e) a + b^{2}} - 2 a); - \frac{1}{2 a} (- 2 a + \sqrt{a^{2} + (- 2 b - 4 c + 4 d - 4 e) a + b^{2}}); \frac{\cos (x)}{2} + \frac{1}{2}) +_C 2 {(\sin (x))}^{- \frac{a + b}{2 a}} {(\cos (x) + 1)}^{\frac{1}{4 a} (2 a + \sqrt{a^{2} + (- 2 b - 4 c - 4 d - 4 e) a + b^{2}})} {(- 1 + \cos (x))}^{\frac{1}{4 a} (2 a + \sqrt{a^{2} + (- 2 b - 4 c + 4 d - 4 e) a + b^{2}})}_{2} F_{1} (\frac{1}{4 a} (\sqrt{a^{2} + (- 2 b - 4 c - 4 d - 4 e) a + b^{2}} + 2 1434 \sqrt{4 a c - b^{2}} + \sqrt{a^{2} + (- 2 b - 4 c + 4 d - 4 e) a + b^{2}} + 2 a), \frac{1}{4 a} (\sqrt{a^{2} + (- 2 b - 4 c - 4 d - 4 e) a + b^{2}} - 2 1434 \sqrt{4 a c - b^{2}} + \sqrt{a^{2} + (- 2 b - 4 c + 4 d - 4 e) a + b^{2}} + 2 a); \frac{1}{2 a} (2 a + \sqrt{a^{2} + (- 2 b - 4 c + 4 d - 4 e) a + b^{2}}); \frac{\cos (x)}{2} + \frac{1}{2})}$

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