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 = 0.47817 (sec), leaf count = 223

$$\{\text{Solve}[\frac{-2a{\tan }^{-1}\left(\frac{ay(x)}{x\sqrt{4b-\frac{a^{2}y(x{)}^2}{x^2}}}\right)+(a+2)(2{\tan }^{-1}\left(\frac{(a+2)y(x)}{x\sqrt{4b-\frac{a^{2}y(x{)}^2}{x^2}}}\right)-i\log (\frac{(a+1)y(x{)}^2}{x^2}+b))}{8(a+1)}=\frac{1}{2}i\log (x)+c_1,y(x)],\text{Solve}[\frac{-2a{\tan }^{-1}\left(\frac{ay(x)}{x\sqrt{4b-\frac{a^{2}y(x{)}^2}{x^2}}}\right)+(a+2)(2{\tan }^{-1}\left(\frac{(a+2)y(x)}{x\sqrt{4b-\frac{a^{2}y(x{)}^2}{x^2}}}\right)+i\log (\frac{(a+1)y(x{)}^2}{x^2}+b))}{8(a+1)}=c_1-\frac{1}{2}i\log (x),y(x)]\}$$ ✓ Maple : cpu = 0.333 (sec), leaf count = 193

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