2.469   ODE No. 469

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

$$ax{y}^{\prime }(x)+by(x)+y(x)y^{\prime }(x{)}^2=0$$ ✓ Mathematica : cpu = 0.327907 (sec), leaf count = 247

$$\{\text{Solve}[\frac{2a{\tanh }^{-1}\left(\frac{\sqrt{a^2-\frac{4by(x{)}^2}{x^2}}}{a}\right)-2(a+2b){\tanh }^{-1}\left(\frac{\sqrt{a^2-\frac{4by(x{)}^2}{x^2}}}{a+2b}\right)+a\log (a+b+\frac{y(x{)}^2}{x^2})+2b\log (a+b+\frac{y(x{)}^2}{x^2})+a\log \left(\frac{y(x{)}^2}{x^2}\right)}{8(a+b)}=c_1-\frac{\log (x)}{2},y(x)],\text{Solve}[\frac{-2a{\tanh }^{-1}\left(\frac{\sqrt{a^2-\frac{4by(x{)}^2}{x^2}}}{a}\right)+2(a+2b){\tanh }^{-1}\left(\frac{\sqrt{a^2-\frac{4by(x{)}^2}{x^2}}}{a+2b}\right)+a\log (a+b+\frac{y(x{)}^2}{x^2})+2b\log (a+b+\frac{y(x{)}^2}{x^2})+a\log \left(\frac{y(x{)}^2}{x^2}\right)}{8(a+b)}=c_1-\frac{\log (x)}{2},y(x)]\}$$

✓ Maple : cpu = 0.099 (sec), leaf count = 242

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