ODE No. 1348

2.1348 ODE No. 1348

Problem in Latex
Mathematica input
Maple input

$y^{″} (x) = - \frac{y (x) (a (x^{4} + 1) + b x^{2})}{x^{4}} - \frac{y^{'} (x)}{x}$ ✗ Mathematica : cpu = 1.26889 (sec), leaf count = 0 , DiﬀerentialRoot result

$\left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{\unicode {f818}''(\unicode {f817}) \unicode {f817}^4+\unicode {f818}'(\unicode {f817}) \unicode {f817}^3+\left (a \unicode {f817}^4+b \unicode {f817}^2+a\right ) \unicode {f818}(\unicode {f817})=0,\unicode {f818}(1)=c_1,\unicode {f818}'(1)=c_2\right \}\right )(x)\right \}\right \}$

✓ Maple : cpu = 0.182 (sec), leaf count = 101

${y (x) =_C 1 H e u n D (0, 2 a + b, 0, 2 a - b, \frac{x^{2} + 1}{x^{2} - 1}) +_C 2 H e u n D (0, 2 a + b, 0, 2 a - b, \frac{x^{2} + 1}{x^{2} - 1}) \int \frac{1}{x} {(H e u n D (0, 2 a + b, 0, 2 a - b, \frac{x^{2} + 1}{x^{2} - 1}))}^{- 2} d x}$

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