3.450   ODE No. 450

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

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

Mathematica: cpu = 0.453058 (sec), leaf count = 26 $$\left\{\{y(x)\to \frac{a^2+c_1^2-x^2}{2c_1}\}\right\}$$

Maple: cpu = 0.795 (sec), leaf count = 51 $$\{y\left(x\right)=\sqrt{a^2-x^2},y\left(x\right)=-\sqrt{a^2-x^2},y\left(x\right)=x^2\mathit{\_}\mathit{C}\mathit{1}-\mathit{\_}\mathit{C}\mathit{1}{a}^2-\frac{1}{4\mathit{\_}\mathit{C}\mathit{1}}\}$$