3.238   ODE No. 238

$$\boxed{{\displaystyle (x(y\left(x\right)+x)+a)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)-y\left(x\right)(y\left(x\right)+x)-b=0}}$$

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

Mathematica: cpu = 0.041505 (sec), leaf count = 192 $$\{\{y(x)\to \frac{1}{x(-\frac{x}{{(a^2+a{x}^2+b{x}^2)}^{3/2}\sqrt{c_1-\frac{1}{(a+b)(a^2+a{x}^2+b{x}^2)}}}-\frac{a}{-a^2-a{x}^2-b{x}^2})}-\frac{a+x^2}{x}\},\{y(x)\to \frac{1}{x(\frac{x}{{(a^2+a{x}^2+b{x}^2)}^{3/2}\sqrt{c_1-\frac{1}{(a+b)(a^2+a{x}^2+b{x}^2)}}}-\frac{a}{-a^2-a{x}^2-b{x}^2})}-\frac{a+x^2}{x}\}\}$$

Maple: cpu = 0.062 (sec), leaf count = 146 $$\{y\left(x\right)=\frac{1}{-a^2+\mathit{\_}\mathit{C}\mathit{1}}(-abx-\mathit{\_}\mathit{C}\mathit{1}x+\sqrt{\mathit{\_}\mathit{C}\mathit{1}{a}^2{x}^2+2\mathit{\_}\mathit{C}\mathit{1}ab{x}^2+\mathit{\_}\mathit{C}\mathit{1}{b}^2{x}^2+\mathit{\_}\mathit{C}\mathit{1}{a}^3+\mathit{\_}\mathit{C}\mathit{1}{a}^{2}b-{\mathit{\_}\mathit{C}\mathit{1}}^{2}a-{\mathit{\_}\mathit{C}\mathit{1}}^{2}b}),y\left(x\right)=-\frac{1}{-a^2+\mathit{\_}\mathit{C}\mathit{1}}(abx+\mathit{\_}\mathit{C}\mathit{1}x+\sqrt{\mathit{\_}\mathit{C}\mathit{1}{a}^2{x}^2+2\mathit{\_}\mathit{C}\mathit{1}ab{x}^2+\mathit{\_}\mathit{C}\mathit{1}{b}^2{x}^2+\mathit{\_}\mathit{C}\mathit{1}{a}^3+\mathit{\_}\mathit{C}\mathit{1}{a}^{2}b-{\mathit{\_}\mathit{C}\mathit{1}}^{2}a-{\mathit{\_}\mathit{C}\mathit{1}}^{2}b})\}$$