ODE No. 669

3.669 ODE No. 669

$\frac{d}{d x} y (x) = 1 / 4 \frac{{(- 2 {(y (x))}^{3 / 2} + 3 e^{x})}^{2} e^{x}}{\sqrt{y (x)}} = 0$

Mathematica: cpu = 0.884112 (sec), leaf count = 264 ${{y (x) \to \frac{(3 e^{3 c_{1} + x} + 2 e^{3 c_{1}} - 2 e^{3 e^{x}} + 3 e^{x + 3 e^{x}})^{2 / 3}}{\sqrt[3]{8 e^{3 c_{1} + 3 e^{x}} + 4 e^{6 c_{1}} + 4 e^{6 e^{x}}}}}, {y (x) \to - \frac{\sqrt[3]{- 1} (3 e^{3 c_{1} + x} + 2 e^{3 c_{1}} - 2 e^{3 e^{x}} + 3 e^{x + 3 e^{x}})^{2 / 3}}{\sqrt[3]{8 e^{3 c_{1} + 3 e^{x}} + 4 e^{6 c_{1}} + 4 e^{6 e^{x}}}}}, {y (x) \to \frac{(- 1)^{2 / 3} (3 e^{3 c_{1} + x} + 2 e^{3 c_{1}} - 2 e^{3 e^{x}} + 3 e^{x + 3 e^{x}})^{2 / 3}}{\sqrt[3]{8 e^{3 c_{1} + 3 e^{x}} + 4 e^{6 c_{1}} + 4 e^{6 e^{x}}}}}}$

Maple: cpu = 0.203 (sec), leaf count = 72 ${_C 1 + 1 e^{- \frac{3 e^{x}}{2} - \frac{9 e^{2 x}}{8}} (2 {(y (x))}^{3 / 2} e^{x} - 2 e^{x} - 3 e^{2 x}) {(e^{\frac{3 e^{x}}{2} - \frac{9 e^{2 x}}{8}})}^{- 1} {(2 {(y (x))}^{3 / 2} e^{x} + 2 e^{x} - 3 e^{2 x})}^{- 1} = 0}$

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