2.424   ODE No. 424

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

$$ay(x)y^{\prime }(x)+bx+x{y}^{\prime }(x{)}^2=0$$ ✓ Mathematica : cpu = 0.384748 (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 = 0.082 (sec), leaf count = 224

$$\{\frac{\mathit{\_}\mathit{C}\mathit{1}}{x}(-ay\left(x\right)+\sqrt{a^2{\left(y\left(x\right)\right)}^2-4b{x}^2}){(-\frac{a}{2x^2}(-a^2{\left(y\left(x\right)\right)}^2+\sqrt{a^2{\left(y\left(x\right)\right)}^2-4b{x}^2}ay\left(x\right)-a{\left(y\left(x\right)\right)}^2+2b{x}^2+\sqrt{a^2{\left(y\left(x\right)\right)}^2-4b{x}^2}y\left(x\right)))}^{-\frac{a+2}{2a+2}}+x=0,\frac{\mathit{\_}\mathit{C}\mathit{1}}{x}(ay\left(x\right)+\sqrt{a^2{\left(y\left(x\right)\right)}^2-4b{x}^2}){\left(\frac{a}{2x^2}(a^2{\left(y\left(x\right)\right)}^2+\sqrt{a^2{\left(y\left(x\right)\right)}^2-4b{x}^2}ay\left(x\right)+a{\left(y\left(x\right)\right)}^2-2b{x}^2+\sqrt{a^2{\left(y\left(x\right)\right)}^2-4b{x}^2}y\left(x\right))\right)}^{-\frac{a+2}{2a+2}}+x=0\}$$