2.1693   ODE No. 1693

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

\[ -h\left (y(x),f(x) y'(x)\right )+f(x) f'(x) y'(x)+f(x)^2 y''(x)=0 \] Mathematica : cpu = 0.829396 (sec), leaf count = 0 , could not solve

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

Maple : cpu = 0.326 (sec), leaf count = 68

\[\left \{y \left (x \right ) = \mathit {ODESolStruc} \left (\textit {\_a} , \left [\left \{\frac {d}{d \textit {\_a}}\mathrm {\_}\mathrm {b}\left (\textit {\_a} \right )=-\textit {\_}b\left (\textit {\_a} \right )^{3} h \left (\textit {\_a} , \frac {1}{\textit {\_}b\left (\textit {\_a} \right )}\right )\right \}, \left \{\textit {\_a} =y \left (x \right ), \textit {\_}b\left (\textit {\_a} \right )=\frac {1}{\left (\frac {d}{d x}y \left (x \right )\right ) f \left (x \right )}\right \}, \left \{x =\RootOf \left (c_{1}+\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} -\left (\int _{}^{\textit {\_Z}}\frac {1}{f \left (\textit {\_f} \right )}d \textit {\_f} \right )\right ), y \left (x \right )=\textit {\_a} \right \}\right ]\right )\right \}\]