3.436   ODE No. 436

$$\boxed{{\displaystyle x^2{\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2-2xy\left(x\right)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+{\left(y\left(x\right)\right)}^2(-x^2+1)-x^4=0}}$$

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

Mathematica: cpu = 0.034504 (sec), leaf count = 26 $$\{\{y(x)\to -x\sinh (x-c_1)\},\{y(x)\to x\sinh (c_1+x)\}\}$$

Maple: cpu = 1.809 (sec), leaf count = 59 $$\{y\left(x\right)=-ix,y\left(x\right)=ix,y\left(x\right)=-\frac{\mathit{\_}\mathit{C}\mathit{1}x}{2{\mathrm{e}}^x}(\frac{{\left({\mathrm{e}}^x\right)}^2}{{\mathit{\_}\mathit{C}\mathit{1}}^2}-1),y\left(x\right)=\frac{x({\left({\mathrm{e}}^x\right)}^2{\mathit{\_}\mathit{C}\mathit{1}}^2-1)}{2{\mathrm{e}}^x\mathit{\_}\mathit{C}\mathit{1}}\}$$