2.1839   ODE No. 1839

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

\[ y'(x)^2-y(x) y''(x)+y^{(3)}(x)=0 \] Mathematica : cpu = 0.0161299 (sec), leaf count = 0 , could not solve

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

Maple : cpu = 1.006 (sec), leaf count = 116

\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {{\rm e}^{\int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C2}}},[ \left \{ {\frac {\rm d}{{\rm d}{\it \_f}}}{\it \_g} \left ( {\it \_f} \right ) =6\,{\frac { \left ( {\it \_g} \left ( {\it \_f} \right ) {\it \_f}+1 \right ) \left ( 1/6+ \left ( {\it \_f}-1/6 \right ) {\it \_g} \left ( {\it \_f} \right ) \right ) {\it \_g} \left ( {\it \_f} \right ) }{{\it \_f}}} \right \} , \left \{ {\it \_f}={\frac {{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{ \left ( y \left ( x \right ) \right ) ^{2}}},{\it \_g} \left ( {\it \_f} \right ) ={\frac { \left ( y \left ( x \right ) \right ) ^{2}{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{ \left ( {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) \right ) y \left ( x \right ) -2\, \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}}} \right \} , \left \{ x=\int \!{\frac {{\it \_g} \left ( {\it \_f} \right ) }{{\it \_f}\,{{\rm e}^{\int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C2}}}}}\,{\rm d}{\it \_f}+{\it \_C1},y \left ( x \right ) ={{\rm e}^{\int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C2}}} \right \} ] \right ) \right \} \]