ODE No. 283

2.283 ODE No. 283

Problem in Latex
Mathematica input
Maple input

$3 (y (x)^{2} - x^{2}) y^{'} (x) + 2 y (x)^{3} - 6 x (x + 1) y (x) - 3 e^{x} = 0$ ✓ Mathematica : cpu = 0.336903 (sec), leaf count = 477

${{y (x) \to - \frac{3 \sqrt[3]{2} e^{2 x} x^{2}}{\sqrt[3]{\sqrt{- 2916 e^{12 x} x^{6} + (- 27 e^{7 x} + 27 c_{1} e^{4 x})^{2}} - 27 e^{7 x} + 27 c_{1} e^{4 x}}} - \frac{e^{- 2 x} \sqrt[3]{\sqrt{- 2916 e^{12 x} x^{6} + (- 27 e^{7 x} + 27 c_{1} e^{4 x})^{2}} - 27 e^{7 x} + 27 c_{1} e^{4 x}}}{3 \sqrt[3]{2}}}, {y (x) \to \frac{3 (1 + i \sqrt{3}) e^{2 x} x^{2}}{2^{2 / 3} \sqrt[3]{\sqrt{- 2916 e^{12 x} x^{6} + (- 27 e^{7 x} + 27 c_{1} e^{4 x})^{2}} - 27 e^{7 x} + 27 c_{1} e^{4 x}}} + \frac{(1 - i \sqrt{3}) e^{- 2 x} \sqrt[3]{\sqrt{- 2916 e^{12 x} x^{6} + (- 27 e^{7 x} + 27 c_{1} e^{4 x})^{2}} - 27 e^{7 x} + 27 c_{1} e^{4 x}}}{6 \sqrt[3]{2}}}, {y (x) \to \frac{3 (1 - i \sqrt{3}) e^{2 x} x^{2}}{2^{2 / 3} \sqrt[3]{\sqrt{- 2916 e^{12 x} x^{6} + (- 27 e^{7 x} + 27 c_{1} e^{4 x})^{2}} - 27 e^{7 x} + 27 c_{1} e^{4 x}}} + \frac{(1 + i \sqrt{3}) e^{- 2 x} \sqrt[3]{\sqrt{- 2916 e^{12 x} x^{6} + (- 27 e^{7 x} + 27 c_{1} e^{4 x})^{2}} - 27 e^{7 x} + 27 c_{1} e^{4 x}}}{6 \sqrt[3]{2}}}}$ ✓ Maple : cpu = 0.059 (sec), leaf count = 407

${y (x) = \frac{1}{4 e^{2 x}} (- 4 x^{2} (1 + i \sqrt{3}) {(e^{2 x})}^{2} + {((4 e^{3 x} - 4_C 1 + 4 \sqrt{- 4 x^{6} {(e^{2 x})}^{2} + {(e^{3 x})}^{2} - 2 e^{3 x}_C 1 + {_C 1}^{2}}) {(e^{2 x})}^{2})}^{\frac{2}{3}} (- 1 + i \sqrt{3})) \frac{1}{\sqrt[3]{- 4 (- e^{3 x} +_C 1 - \sqrt{- 4 x^{6} {(e^{2 x})}^{2} + {(e^{3 x})}^{2} - 2 e^{3 x}_C 1 + {_C 1}^{2}}) {(e^{2 x})}^{2}}}, y (x) = \frac{1}{2 e^{2 x}} (4 x^{2} {(e^{2 x})}^{2} + {((4 e^{3 x} - 4_C 1 + 4 \sqrt{- 4 x^{6} {(e^{2 x})}^{2} + {(e^{3 x})}^{2} - 2 e^{3 x}_C 1 + {_C 1}^{2}}) {(e^{2 x})}^{2})}^{\frac{2}{3}}) \frac{1}{\sqrt[3]{- 4 (- e^{3 x} +_C 1 - \sqrt{- 4 x^{6} {(e^{2 x})}^{2} + {(e^{3 x})}^{2} - 2 e^{3 x}_C 1 + {_C 1}^{2}}) {(e^{2 x})}^{2}}}, y (x) = - \frac{1}{4 e^{2 x}} (- 4 x^{2} (- 1 + i \sqrt{3}) {(e^{2 x})}^{2} + (1 + i \sqrt{3}) {((4 e^{3 x} - 4_C 1 + 4 \sqrt{- 4 x^{6} {(e^{2 x})}^{2} + {(e^{3 x})}^{2} - 2 e^{3 x}_C 1 + {_C 1}^{2}}) {(e^{2 x})}^{2})}^{\frac{2}{3}}) \frac{1}{\sqrt[3]{- 4 (- e^{3 x} +_C 1 - \sqrt{- 4 x^{6} {(e^{2 x})}^{2} + {(e^{3 x})}^{2} - 2 e^{3 x}_C 1 + {_C 1}^{2}}) {(e^{2 x})}^{2}}}}$

[next] [prev] [prev-tail] [front] [up]