2.238   ODE No. 238

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

$$(a+x(y(x)+x))y^{\prime }(x)-b-y(x)(y(x)+x)=0$$ ✓ Mathematica : cpu = 0.0441271 (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 = 0.081 (sec), leaf count = 133

$$\{y\left(x\right)=\frac{1}{\mathit{\_}\mathit{C}\mathit{1}{a}^2-1}(\mathit{\_}\mathit{C}\mathit{1}abx+\sqrt{\mathit{\_}\mathit{C}\mathit{1}{a}^2{x}^2+2\mathit{\_}\mathit{C}\mathit{1}ab{x}^2+\mathit{\_}\mathit{C}\mathit{1}{b}^2{x}^2+\mathit{\_}\mathit{C}\mathit{1}{a}^3+\mathit{\_}\mathit{C}\mathit{1}{a}^{2}b-a-b}+x),y\left(x\right)=-\frac{1}{\mathit{\_}\mathit{C}\mathit{1}{a}^2-1}(-\mathit{\_}\mathit{C}\mathit{1}abx+\sqrt{\mathit{\_}\mathit{C}\mathit{1}{a}^2{x}^2+2\mathit{\_}\mathit{C}\mathit{1}ab{x}^2+\mathit{\_}\mathit{C}\mathit{1}{b}^2{x}^2+\mathit{\_}\mathit{C}\mathit{1}{a}^3+\mathit{\_}\mathit{C}\mathit{1}{a}^{2}b-a-b}-x)\}$$