2.1406   ODE No. 1406

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

$$y^{″}(x)=-\frac{27xy(x)}{16{(x^3-1)}^2}$$ ✓ Mathematica : cpu = 1.68214 (sec), leaf count = 258

$$\left\{\{y(x)\to \frac{\sqrt{2}{c}_2(1-x{)}^{3/4}\sqrt[4]{x^2+x+1}{\int }_1^x\frac{\sqrt{\sqrt{3}K[1]+\sqrt{2K[1]-i\sqrt{3}+1}\sqrt{2K[1]+i\sqrt{3}+1}+\sqrt{3}}}{2(1-K[1]{)}^{3/2}\sqrt{K[1{]}^2+K[1]+1}}dK[1]}{\sqrt[4]{\sqrt{3}x+\sqrt{2x-i\sqrt{3}+1}\sqrt{2x+i\sqrt{3}+1}+\sqrt{3}}}+\frac{\sqrt{2}{c}_1(1-x{)}^{3/4}\sqrt[4]{x^2+x+1}}{\sqrt[4]{\sqrt{3}x+\sqrt{2x-i\sqrt{3}+1}\sqrt{2x+i\sqrt{3}+1}+\sqrt{3}}}\}\right\}$$ ✓ Maple : cpu = 0.163 (sec), leaf count = 44

$$\{y\left(x\right)={(x^3-1)}^{\frac{1}{4}}(c_1\mathrm{LegendreP}(-\frac{1}{6},\frac{1}{3},\sqrt{-x^3+1})+c_2\mathrm{LegendreQ}(-\frac{1}{6},\frac{1}{3},\sqrt{-x^3+1}))\sqrt{x}\}$$