3.142   ODE No. 142

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

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

Mathematica: cpu = 0.181523 (sec), leaf count = 113 $$\left\{\{y(x)\to -\frac{\frac{1}{a^3{x}^2}+c_1(\frac{e^{ax}(a^{2}x+a(ax-2))}{x}-\frac{e^{ax}(ax(ax-2)+2)}{x^2}+\frac{a{e}^{ax}(ax(ax-2)+2)}{x})}{\frac{c_1{e}^{ax}(ax(ax-2)+2)}{x}-\frac{1}{a^{3}x}}\}\right\}$$

Maple: cpu = 0.078 (sec), leaf count = 61 $$\{y\left(x\right)=-\frac{(a^3{x}^3-a^2{x}^2+2ax-2){\mathrm{e}}^{ax}-\mathit{\_}\mathit{C}\mathit{1}}{x((a^2{x}^2-2ax+2){\mathrm{e}}^{ax}+\mathit{\_}\mathit{C}\mathit{1})}\}$$