3.218   ODE No. 218

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

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

Mathematica: cpu = 0.102513 (sec), leaf count = 257 $$\{\{y(x)\to x^2+\frac{1}{-\frac{1}{2x^2}-\frac{\frac{1}{2}-\frac{i}{2}}{\sqrt{2}{x}^2\sqrt{x^2\sinh \left(\frac{2c_1}{9}\right)+x^2\cosh \left(\frac{2c_1}{9}\right)-i}}}\},\{y(x)\to x^2+\frac{1}{-\frac{1}{2x^2}+\frac{\frac{1}{2}-\frac{i}{2}}{\sqrt{2}{x}^2\sqrt{x^2\sinh \left(\frac{2c_1}{9}\right)+x^2\cosh \left(\frac{2c_1}{9}\right)-i}}}\},\{y(x)\to x^2+\frac{1}{-\frac{1}{2x^2}-\frac{\frac{1}{2}+\frac{i}{2}}{\sqrt{2}{x}^2\sqrt{x^2\sinh \left(\frac{2c_1}{9}\right)+x^2\cosh \left(\frac{2c_1}{9}\right)+i}}}\},\{y(x)\to x^2+\frac{1}{-\frac{1}{2x^2}+\frac{\frac{1}{2}+\frac{i}{2}}{\sqrt{2}{x}^2\sqrt{x^2\sinh \left(\frac{2c_1}{9}\right)+x^2\cosh \left(\frac{2c_1}{9}\right)+i}}}\}\}$$

Maple: cpu = 0.140 (sec), leaf count = 53 $$\{y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{1}}{2}(\mathit{\_}\mathit{C}\mathit{1}-\sqrt{{\mathit{\_}\mathit{C}\mathit{1}}^2-4x^2})-x^2,y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{1}}{2}(\mathit{\_}\mathit{C}\mathit{1}+\sqrt{{\mathit{\_}\mathit{C}\mathit{1}}^2-4x^2})-x^2\}$$