3.181   ODE No. 181

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

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

Mathematica: cpu = 0.011501 (sec), leaf count = 347 $$\left\{\{y(x)\to -\frac{\frac{i\sqrt{\frac{2}{\pi }}{c}_1\sinh \left(\frac{\sqrt{-a}}{x}\right)}{\sqrt{-\frac{i\sqrt{-a}}{x}}}+\frac{i\sqrt{-a}(-\frac{\sqrt{\frac{2}{\pi }}{c}_1\cosh \left(\frac{\sqrt{-a}}{x}\right)}{\sqrt{-\frac{i\sqrt{-a}}{x}}}+\frac{\sqrt{\frac{2}{\pi }}{c}_1(-\frac{\sqrt{-a}x\sinh \left(\frac{\sqrt{-a}}{x}\right)}{a}-\cosh \left(\frac{\sqrt{-a}}{x}\right))}{\sqrt{-\frac{i\sqrt{-a}}{x}}}-\frac{2\sqrt{\frac{2}{\pi }}(i\sinh \left(\frac{\sqrt{-a}}{x}\right)+\frac{i\sqrt{-a}x\cosh \left(\frac{\sqrt{-a}}{x}\right)}{a})}{\sqrt{-\frac{i\sqrt{-a}}{x}}})}{x}}{2x(\frac{\sqrt{\frac{2}{\pi }}\cosh \left(\frac{\sqrt{-a}}{x}\right)}{\sqrt{-\frac{i\sqrt{-a}}{x}}}-\frac{i\sqrt{\frac{2}{\pi }}{c}_1\sinh \left(\frac{\sqrt{-a}}{x}\right)}{\sqrt{-\frac{i\sqrt{-a}}{x}}})}\}\right\}$$

Maple: cpu = 0.063 (sec), leaf count = 30 $$\{y\left(x\right)=-\frac{1}{x^2}(\tan \left(\frac{\mathit{\_}\mathit{C}\mathit{1}x-1}{x}\sqrt{a}\right)\sqrt{a}-x)\}$$