3.424   ODE No. 424

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

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

Mathematica: cpu = 0.378048 (sec), leaf count = 223 $$\{\text{Solve}[\frac{-2a{\tan }^{-1}\left(\frac{ay(x)}{x\sqrt{4b-\frac{a^{2}y(x{)}^2}{x^2}}}\right)+(a+2)(2{\tan }^{-1}\left(\frac{(a+2)y(x)}{x\sqrt{4b-\frac{a^{2}y(x{)}^2}{x^2}}}\right)-i\log (\frac{(a+1)y(x{)}^2}{x^2}+b))}{8(a+1)}=c_1+\frac{1}{2}i\log (x),y(x)],\text{Solve}[\frac{-2a{\tan }^{-1}\left(\frac{ay(x)}{x\sqrt{4b-\frac{a^{2}y(x{)}^2}{x^2}}}\right)+(a+2)(2{\tan }^{-1}\left(\frac{(a+2)y(x)}{x\sqrt{4b-\frac{a^{2}y(x{)}^2}{x^2}}}\right)+i\log (\frac{(a+1)y(x{)}^2}{x^2}+b))}{8(a+1)}=c_1-\frac{1}{2}i\log (x),y(x)]\}$$

Maple: cpu = 0.546 (sec), leaf count = 224 $$\{\frac{\mathit{\_}\mathit{C}\mathit{1}}{x}{\left(\frac{a}{2x^2}(a^2{\left(y\left(x\right)\right)}^2+\sqrt{a^2{\left(y\left(x\right)\right)}^2-4b{x}^2}ay\left(x\right)+a{\left(y\left(x\right)\right)}^2-2b{x}^2+\sqrt{a^2{\left(y\left(x\right)\right)}^2-4b{x}^2}y\left(x\right))\right)}^{-\frac{a+2}{2a+2}}(ay\left(x\right)+\sqrt{a^2{\left(y\left(x\right)\right)}^2-4b{x}^2})+x=0,\frac{\mathit{\_}\mathit{C}\mathit{1}}{x}(-ay\left(x\right)+\sqrt{a^2{\left(y\left(x\right)\right)}^2-4b{x}^2}){(-\frac{a}{2x^2}(-a^2{\left(y\left(x\right)\right)}^2+\sqrt{a^2{\left(y\left(x\right)\right)}^2-4b{x}^2}ay\left(x\right)-a{\left(y\left(x\right)\right)}^2+2b{x}^2+\sqrt{a^2{\left(y\left(x\right)\right)}^2-4b{x}^2}y\left(x\right)))}^{-\frac{a+2}{2a+2}}+x=0\}$$