8.80   ODE No. 1670

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

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

Mathematica: cpu = 90.651011 (sec), leaf count = 50 $$\left\{\{y(x)\to x({\int }_1^x\frac{\sqrt{-\frac{b}{a}}\tan (c_1-a\sqrt{-\frac{b}{a}}K[2])}{K[2{]}^2}dK[2]+c_2)\}\right\}$$

Maple: cpu = 0.281 (sec), leaf count = 35 $$\{y\left(x\right)=(\int \frac{i}{x^2}\tan (-i\sqrt{a}\sqrt{b}x+\mathit{\_}\mathit{C}\mathit{1})\sqrt{b}\frac{1}{\sqrt{a}}\mathrm{d}x+\mathit{\_}\mathit{C}\mathit{2})x\}$$