2.1708   ODE No. 1708

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

\[ a y(x) y'(x)-2 a y(x)^2+b y(x)^3+y(x) y''(x)-y'(x)^2=0 \] Mathematica : cpu = 43.574 (sec), leaf count = 0 , could not solve

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

Maple : cpu = 2.422 (sec), leaf count = 73

\[\left \{y \left (x \right ) = \mathit {ODESolStruc} \left (\textit {\_a} , \left [\left \{\textit {\_}b\left (\textit {\_a} \right ) \left (\frac {d}{d \textit {\_a}}\mathrm {\_}\mathrm {b}\left (\textit {\_a} \right )\right )-\frac {-\textit {\_a}^{3} b +2 \textit {\_a}^{2} a -\textit {\_a} a \textit {\_}b\left (\textit {\_a} \right )+\textit {\_}b\left (\textit {\_a} \right )^{2}}{\textit {\_a}}=0\right \}, \left \{\textit {\_a} =y \left (x \right ), \textit {\_}b\left (\textit {\_a} \right )=\frac {d}{d x}y \left (x \right )\right \}, \left \{x =c_{1}+\int \frac {1}{\textit {\_}b\left (\textit {\_a} \right )}d \textit {\_a} , y \left (x \right )=\textit {\_a} \right \}\right ]\right )\right \}\]