8.86   ODE No. 1676

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

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

Mathematica: cpu = 54.698946 (sec), leaf count = 133 $$\left\{\{y(x)\to x(c_2+{\int }_1^x\frac{i\sqrt{a}\sqrt{b}{Y}_1(-i\sqrt{a}\sqrt{b}K[2])-i\sqrt{a}\sqrt{b}{c}_1{J}_1(i\sqrt{a}\sqrt{b}K[2])}{aK[2](c_1{J}_0(i\sqrt{a}\sqrt{b}K[2])+Y_0(-i\sqrt{a}\sqrt{b}K[2]))}dK[2])\}\right\}$$

Maple: cpu = 0.920 (sec), leaf count = 110 $$\{y\left(x\right)=(\int -\frac{\mathit{\_}\mathit{C}\mathit{1}}{ax}{\mathit{Y}}_1\left(\sqrt{-ab}x\right)\sqrt{-ab}{(\mathit{\_}\mathit{C}\mathit{1}{\mathit{Y}}_0\left(\sqrt{-ab}x\right)+{\mathit{J}}_0\left(\sqrt{-ab}x\right))}^{-1}-\frac{1}{ax}{\mathit{J}}_1\left(\sqrt{-ab}x\right)\sqrt{-ab}{(\mathit{\_}\mathit{C}\mathit{1}{\mathit{Y}}_0\left(\sqrt{-ab}x\right)+{\mathit{J}}_0\left(\sqrt{-ab}x\right))}^{-1}\mathrm{d}x+\mathit{\_}\mathit{C}\mathit{2})x\}$$