3.469   ODE No. 469

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

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

Mathematica: cpu = 0.945120 (sec), leaf count = 317 $$\{\text{Solve}[\frac{(\sqrt{a^2-\frac{4by(x{)}^2}{x^2}}-a)(\sqrt{a^2-\frac{4by(x{)}^2}{x^2}}+a+2b)(a\log (\sqrt{a^2-\frac{4by(x{)}^2}{x^2}}-a)+(a+2b)\log (\sqrt{a^2-\frac{4by(x{)}^2}{x^2}}+a+2b))}{8b(a+b)(\sqrt{a^2-\frac{4by(x{)}^2}{x^2}}-a-\frac{2y(x{)}^2}{x^2})}=c_1-\frac{\log (x)}{2},y(x)],\text{Solve}[\frac{(-\sqrt{a^2-\frac{4by(x{)}^2}{x^2}}+a+2b)(\sqrt{a^2-\frac{4by(x{)}^2}{x^2}}+a)(a\log (\sqrt{a^2-\frac{4by(x{)}^2}{x^2}}+a)+(a+2b)\log (\sqrt{a^2-\frac{4by(x{)}^2}{x^2}}-a-2b))}{8b(a+b)(\sqrt{a^2-\frac{4by(x{)}^2}{x^2}}+a+\frac{2y(x{)}^2}{x^2})}=c_1-\frac{\log (x)}{2},y(x)]\}$$

Maple: cpu = 0.639 (sec), leaf count = 242 $$\{\frac{\mathit{\_}\mathit{C}\mathit{1}x}{{\left(y\left(x\right)\right)}^2}{(-\frac{1}{2y\left(x\right)}(ax+\sqrt{a^2{x}^2-4b{\left(y\left(x\right)\right)}^2}))}^{-\frac{a}{a+b}}(ax+\sqrt{a^2{x}^2-4b{\left(y\left(x\right)\right)}^2}){\left(\frac{a}{2{\left(y\left(x\right)\right)}^2}(a{x}^2+\sqrt{a^2{x}^2-4b{\left(y\left(x\right)\right)}^2}x+2{\left(y\left(x\right)\right)}^2)\right)}^{-\frac{a+2b}{2a+2b}}+x=0,\frac{\mathit{\_}\mathit{C}\mathit{1}x}{{\left(y\left(x\right)\right)}^2}{(-\frac{a}{2{\left(y\left(x\right)\right)}^2}(-a{x}^2+\sqrt{a^2{x}^2-4b{\left(y\left(x\right)\right)}^2}x-2{\left(y\left(x\right)\right)}^2))}^{-\frac{a+2b}{2a+2b}}(-ax+\sqrt{a^2{x}^2-4b{\left(y\left(x\right)\right)}^2}){\left(\frac{1}{2y\left(x\right)}(-ax+\sqrt{a^2{x}^2-4b{\left(y\left(x\right)\right)}^2})\right)}^{-\frac{a}{a+b}}+x=0\}$$