2.1408   ODE No. 1408

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

$$y^{″}(x)=-\frac{y(x)(A{x}^2+B)}{x(x^2-\text{a1})(x^2-\text{a2})(x^2-\text{a3})}-\frac{y^{\prime }(x)(x^2((x^2-\text{a1})(x^2-\text{a2})+(x^2-\text{a1})(x^2-\text{a3})+(x^2-\text{a2})(x^2-\text{a3}))-(x^2-\text{a1})(x^2-\text{a2})(x^2-\text{a3}))}{x(x^2-\text{a1})(x^2-\text{a2})(x^2-\text{a3})}$$ ✗ Mathematica : cpu = 61.2665 (sec), leaf count = 0 , DifferentialRoot result

$$\text{left {left {y(x)to text {DifferentialRoot}left ({unicode {f818},unicode {f817}}unicode {f4a1}left {left (A unicode {f817}^2+Bright ) unicode {f818}(unicode {f817})+left (2 unicode {f817}^6-text {a1} unicode {f817}^4-text {a2} unicode {f817}^4-text {a3} unicode {f817}^4+text {a1} text {a2} text {a3}right ) unicode {f818}'(unicode {f817})-unicode {f817} left (text {a1}-unicode {f817}^2right ) left (text {a2}-unicode {f817}^2right ) left (text {a3}-unicode {f817}^2right ) unicode {f818}''(unicode {f817})=0,unicode {f818}(1)=c\_1,unicode {f818}'(1)=c\_2right }right )(x)right }right }}$$

✗ Maple : cpu = 0. (sec), leaf count = 0 , result contains DESol

$$\{y\left(x\right)=\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}(\{\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}\mathit{\_}\mathit{Y}\left(x\right)+\frac{(x^2((x^2-\mathit{a}\mathit{1})(x^2-\mathit{a}\mathit{2})+(x^2-\mathit{a}\mathit{2})(x^2-\mathit{a}\mathit{3})+(x^2-\mathit{a}\mathit{3})(x^2-\mathit{a}\mathit{1}))-(x^2-\mathit{a}\mathit{1})(x^2-\mathit{a}\mathit{2})(x^2-\mathit{a}\mathit{3}))\frac{\mathrm{d}}{\mathrm{d}x}\mathit{\_}\mathit{Y}\left(x\right)}{(x^2-\mathit{a}\mathit{1})(x^2-\mathit{a}\mathit{2})x(x^2-\mathit{a}\mathit{3})}+\frac{(A{x}^2+B)\mathit{\_}\mathit{Y}\left(x\right)}{(x^2-\mathit{a}\mathit{1})(x^2-\mathit{a}\mathit{2})x(x^2-\mathit{a}\mathit{3})}\},\left\{\mathit{\_}\mathit{Y}\left(x\right)\right\})\}$$