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 = 41.9911 (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 = 0.787 (sec), leaf count = 56

\[\left \{y \left (x \right ) = \mathit {ODESolStruc} \left (\textit {\_a} , \left [\left \{\textit {\_}b\left (\textit {\_a} \right )^{2} h \left (\textit {\_a} \right )+\textit {\_}b\left (\textit {\_a} \right ) \left (\frac {d}{d \textit {\_a}}\mathrm {\_}\mathrm {b}\left (\textit {\_a} \right )\right )+\textit {\_}b\left (\textit {\_a} \right )+k \left (\textit {\_a} \right )=0\right \}, \left \{\textit {\_a} =y \left (x \right ), \textit {\_}b\left (\textit {\_a} \right )=\frac {d}{d x}y \left (x \right )\right \}, \left \{x =c_{1}+\int \frac {1}{\textit {\_}b\left (\textit {\_a} \right )}d \textit {\_a} , y \left (x \right )=\textit {\_a} \right \}\right ]\right )\right \}\]