2.1684   ODE No. 1684

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

\[ x y(x) \left (a-2 x^2 y(x)^2+3 x y(x)\right )+b+2 x^3 y''(x)+x^2 (2 x y(x)+9) y'(x)=0 \] Mathematica : cpu = 54.0549 (sec), leaf count = 0 , could not solve

DSolve[b + x*y[x]*(a + 3*x*y[x] - 2*x^2*y[x]^2) + x^2*(9 + 2*x*y[x])*Derivative[1][y][x] + 2*x^3*Derivative[2][y][x] == 0, y[x], x]

Maple : cpu = 2.791 (sec), leaf count = 100

\[\left \{y \left (x \right ) = \mathit {ODESolStruc} \left (\textit {\_a} \,{\mathrm e}^{c_{1}+\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a}}, \left [\left \{\frac {d}{d \textit {\_a}}\mathrm {\_}\mathrm {b}\left (\textit {\_a} \right )=\frac {\left (-2 \textit {\_a} +\left (-2 \textit {\_a}^{3}+\textit {\_a}^{2}+\left (a -5\right ) \textit {\_a} +b \right ) \textit {\_}b\left (\textit {\_a} \right )-3\right ) \textit {\_}b\left (\textit {\_a} \right )^{2}}{2}\right \}, \left \{\textit {\_a} =x y \left (x \right ), \textit {\_}b\left (\textit {\_a} \right )=-\frac {1}{\left (x \left (\frac {d}{d x}y \left (x \right )\right )+y \left (x \right )\right ) x}\right \}, \left \{x ={\mathrm e}^{-c_{1}+\int -\textit {\_}b\left (\textit {\_a} \right )d \textit {\_a}}, y \left (x \right )=\textit {\_a} \,{\mathrm e}^{c_{1}+\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a}}\right \}\right ]\right )\right \}\]