4.402   ODE No. 1402

$$\boxed{{\displaystyle \frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)=-\frac{((1-4a)x^2-1)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)}{x(x^2-1)}-\frac{((-v^2+x^2){(x^2-1)}^2+4a(a+1)x^4-2a{x}^2(x^2-1))y\left(x\right)}{x^2{(x^2-1)}^2}=0}}$$

1. Problem in Latex
2. Mathematica input
3. Maple input

Mathematica: cpu = 4.464067 (sec), leaf count = 127 $$\text{left {left {y(x)to text {DifferentialRoot}left ({unicode {f818},unicode {f817}}unicode {f4a1}left {left (unicode {f817}^6+4 a^2 unicode {f817}^4-v^2 unicode {f817}^4+2 a unicode {f817}^4-2 unicode {f817}^4+2 v^2 unicode {f817}^2+2 a unicode {f817}^2+unicode {f817}^2-v^2right ) unicode {f818}(unicode {f817})+left (-4 a unicode {f817}^5+unicode {f817}^5+4 a unicode {f817}^3-2 unicode {f817}^3+unicode {f817}right ) unicode {f818}'(unicode {f817})+left (unicode {f817}^6-2 unicode {f817}^4+unicode {f817}^2right ) unicode {f818}''(unicode {f817})=0,unicode {f818}(2)=c\_1,unicode {f818}'(2)=c\_2right }right )(x)right }right }}$$

Maple: cpu = 0.218 (sec), leaf count = 69 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{x}^v{(x^2-1)}^a(x^2-1)\mathit{H}\mathit{e}\mathit{u}\mathit{n}\mathit{C}(0,v,1,\frac{1}{4},\frac{a}{2}+\frac{1}{4},x^2)+\mathit{\_}\mathit{C}\mathit{2}{x}^{-v}{(x^2-1)}^a(x^2-1)\mathit{H}\mathit{e}\mathit{u}\mathit{n}\mathit{C}(0,-v,1,\frac{1}{4},\frac{a}{2}+\frac{1}{4},x^2)\}$$