2.1620   ODE No. 1620

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

\[ y''(x)+y(x) y'(x)-y(x)^3=0 \] Mathematica : cpu = 122.372 (sec), leaf count = 0 , could not solve

DSolve[-y[x]^3 + y[x]*Derivative[1][y][x] + Derivative[2][y][x] == 0, y[x], x]

Maple : cpu = 0.125 (sec), leaf count = 253

\[ \left \{ \int ^{y \left ( x \right ) }\! \left ( {\frac {{{\it \_a}}^{2}}{2}}+{\frac {1}{2} \left ( \sqrt [3]{{\it \_C1}+\sqrt {{{\it \_a}}^{6}+{{\it \_C1}}^{2}}}-{{{\it \_a}}^{2}{\frac {1}{\sqrt [3]{{\it \_C1}+\sqrt {{{\it \_a}}^{6}+{{\it \_C1}}^{2}}}}}} \right ) ^{2}} \right ) ^{-1}{d{\it \_a}}-x-{\it \_C2}=0,\int ^{y \left ( x \right ) }\! \left ( {\frac {{{\it \_a}}^{2}}{2}}+{\frac {1}{2} \left ( -{\frac {1}{2}\sqrt [3]{{\it \_C1}+\sqrt {{{\it \_a}}^{6}+{{\it \_C1}}^{2}}}}+{\frac {{{\it \_a}}^{2}}{2}{\frac {1}{\sqrt [3]{{\it \_C1}+\sqrt {{{\it \_a}}^{6}+{{\it \_C1}}^{2}}}}}}-{\frac {i}{2}}\sqrt {3} \left ( \sqrt [3]{{\it \_C1}+\sqrt {{{\it \_a}}^{6}+{{\it \_C1}}^{2}}}+{{{\it \_a}}^{2}{\frac {1}{\sqrt [3]{{\it \_C1}+\sqrt {{{\it \_a}}^{6}+{{\it \_C1}}^{2}}}}}} \right ) \right ) ^{2}} \right ) ^{-1}{d{\it \_a}}-x-{\it \_C2}=0,\int ^{y \left ( x \right ) }\! \left ( {\frac {{{\it \_a}}^{2}}{2}}+{\frac {1}{2} \left ( -{\frac {1}{2}\sqrt [3]{{\it \_C1}+\sqrt {{{\it \_a}}^{6}+{{\it \_C1}}^{2}}}}+{\frac {{{\it \_a}}^{2}}{2}{\frac {1}{\sqrt [3]{{\it \_C1}+\sqrt {{{\it \_a}}^{6}+{{\it \_C1}}^{2}}}}}}+{\frac {i}{2}}\sqrt {3} \left ( \sqrt [3]{{\it \_C1}+\sqrt {{{\it \_a}}^{6}+{{\it \_C1}}^{2}}}+{{{\it \_a}}^{2}{\frac {1}{\sqrt [3]{{\it \_C1}+\sqrt {{{\it \_a}}^{6}+{{\it \_C1}}^{2}}}}}} \right ) \right ) ^{2}} \right ) ^{-1}{d{\it \_a}}-x-{\it \_C2}=0 \right \} \]