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 = 0.265312 (sec), leaf count = 157

$$\{\text{Solve}[\frac{(a+2b)\log (-\sqrt{a^2-\frac{4by(x{)}^2}{x^2}}+a+2b)+a\log (\sqrt{a^2-\frac{4by(x{)}^2}{x^2}}+a)}{4(a+b)}=-\frac{\log (x)}{2}+c_1,y(x)],\text{Solve}[\frac{a\log (a-\sqrt{a^2-\frac{4by(x{)}^2}{x^2}})+(a+2b)\log (\sqrt{a^2-\frac{4by(x{)}^2}{x^2}}+a+2b)}{4(a+b)}=-\frac{\log (x)}{2}+c_1,y(x)]\}$$ ✓ Maple : cpu = 0.321 (sec), leaf count = 264

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