3.100   ODE No. 100

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

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

Mathematica: cpu = 0.007501 (sec), leaf count = 157 $$\left\{\{y(x)\to -\frac{c_1{J}_1\left(2i\sqrt{-a}\sqrt{x}\right)+i\sqrt{-a}\sqrt{x}(c_1{J}_0\left(2i\sqrt{-a}\sqrt{x}\right)-c_1{J}_2\left(2i\sqrt{-a}\sqrt{x}\right)-2J_0\left(2i\sqrt{-a}\sqrt{x}\right))}{2x(J_1\left(2i\sqrt{-a}\sqrt{x}\right)-c_1{J}_1\left(2i\sqrt{-a}\sqrt{x}\right))}\}\right\}$$

Maple: cpu = 0.062 (sec), leaf count = 59 $$\{y\left(x\right)=1\sqrt{a}({\mathit{J}}_0\left(2\sqrt{a}\sqrt{x}\right)\mathit{\_}\mathit{C}\mathit{1}+{\mathit{Y}}_0\left(2\sqrt{a}\sqrt{x}\right))\frac{1}{\sqrt{x}}{(\mathit{\_}\mathit{C}\mathit{1}{\mathit{J}}_1\left(2\sqrt{a}\sqrt{x}\right)+{\mathit{Y}}_1\left(2\sqrt{a}\sqrt{x}\right))}^{-1}\}$$