2.164   ODE No. 164

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

$$2a^{2}x+2x^2{y}^{\prime }(x)-2y(x{)}^2-3xy(x)=0$$ ✓ Mathematica : cpu = 0.0798587 (sec), leaf count = 131

$$\left\{\{y(x)\to -\frac{x^2(c_1(\frac{a{e}^{-\frac{2a}{\sqrt{x}}}}{x}+\frac{e^{-\frac{2a}{\sqrt{x}}}}{2\sqrt{x}})-\frac{e^{\frac{2a}{\sqrt{x}}}}{4a\sqrt{x}}+\frac{e^{\frac{2a}{\sqrt{x}}}}{2x})}{c_1\sqrt{x}{e}^{-\frac{2a}{\sqrt{x}}}-\frac{\sqrt{x}{e}^{\frac{2a}{\sqrt{x}}}}{2a}}\}\right\}$$

✓ Maple : cpu = 0.216 (sec), leaf count = 102

$$\{y\left(x\right)=1((-2x\mathit{\_}\mathit{C}\mathit{1}\sqrt{-\frac{a^2}{x}}-x)\sin \left(2\sqrt{-\frac{a^2}{x}}\right)-x(\mathit{\_}\mathit{C}\mathit{1}-2\sqrt{-\frac{a^2}{x}})\cos \left(2\sqrt{-\frac{a^2}{x}}\right)){(2\cos \left(2\sqrt{-\frac{a^2}{x}}\right)\mathit{\_}\mathit{C}\mathit{1}+2\sin \left(2\sqrt{-\frac{a^2}{x}}\right))}^{-1}\}$$