3.281   ODE No. 281

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

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

Mathematica: cpu = 0.062508 (sec), leaf count = 75 $$\{\{y(x)\to \frac{1}{2}(e^{c_1}-\sqrt{4e^{c_1}x+e^{2c_1}-4x^2})\},\{y(x)\to \frac{1}{2}(\sqrt{4e^{c_1}x+e^{2c_1}-4x^2}+e^{c_1})\}\}$$

Maple: cpu = 0.047 (sec), leaf count = 53 $$\{y\left(x\right)=\frac{1}{2\mathit{\_}\mathit{C}\mathit{1}}(1+\sqrt{-4{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2+4\mathit{\_}\mathit{C}\mathit{1}x+1}),y\left(x\right)=-\frac{1}{2\mathit{\_}\mathit{C}\mathit{1}}(-1+\sqrt{-4{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2+4\mathit{\_}\mathit{C}\mathit{1}x+1})\}$$