2.1644   ODE No. 1644

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

\[ h(y(x)) y'(x)^2+j(y(x)) y'(x)+k(y(x))+y''(x)=0 \] Mathematica : cpu = 81.9496 (sec), leaf count = 0 , could not solve

DSolve[k[y[x]] + j[y[x]]*Derivative[1][y][x] + h[y[x]]*Derivative[1][y][x]^2 + Derivative[2][y][x] == 0, y[x], x]

Maple : cpu = 0.66 (sec), leaf count = 56

\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_a},[ \left \{ \left ( {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) \right ) {\it \_b} \left ( {\it \_a} \right ) +h \left ( {\it \_a} \right ) \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}+{\it \_b} \left ( {\it \_a} \right ) +k \left ( {\it \_a} \right ) =0 \right \} , \left \{ {\it \_a}=y \left ( x \right ) ,{\it \_b} \left ( {\it \_a} \right ) ={\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right \} , \left \{ x=\int \! \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{-1}\,{\rm d}{\it \_a}+{\it \_C1},y \left ( x \right ) ={\it \_a} \right \} ] \right ) \right \} \]