2.1687   ODE No. 1687

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

$$x^4{y}^{″}(x)-x(x^2+2y(x))y^{\prime }(x)+4y(x{)}^2=0$$ ✓ Mathematica : cpu = 0.068986 (sec), leaf count = 262

$$\left\{\{y(x)\to -\frac{x^3(i(-\frac{\sqrt{-c_1-1}}{\sqrt{c_1}}+\frac{i}{\sqrt{c_1}})\sqrt{c_1}{c}_2{x}^{-1+i(-\frac{\sqrt{-c_1-1}}{\sqrt{c_1}}+\frac{i}{\sqrt{c_1}})\sqrt{c_1}}+i(\frac{\sqrt{-c_1-1}}{\sqrt{c_1}}+\frac{i}{\sqrt{c_1}})\sqrt{c_1}{x}^{-1+i(\frac{\sqrt{-c_1-1}}{\sqrt{c_1}}+\frac{i}{\sqrt{c_1}})\sqrt{c_1}})}{c_2{x}^{i(-\frac{\sqrt{-c_1-1}}{\sqrt{c_1}}+\frac{i}{\sqrt{c_1}})\sqrt{c_1}}+x^{i(\frac{\sqrt{-c_1-1}}{\sqrt{c_1}}+\frac{i}{\sqrt{c_1}})\sqrt{c_1}}}\}\right\}$$

✓ Maple : cpu = 0.235 (sec), leaf count = 23

$$\{y\left(x\right)=\tanh (-\ln \left(x\right)\mathit{\_}\mathit{C}\mathit{1}+\mathit{\_}\mathit{C}\mathit{2}\mathit{\_}\mathit{C}\mathit{1})x^2\mathit{\_}\mathit{C}\mathit{1}+x^2\}$$