2.1624   ODE No. 1624

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

\[ y(x) \left (a f(x)^2-\frac {f''(x)}{f(x)}+3 f'(x)+\frac {3 f'(x)^2}{f(x)^2}\right )+b f(x)^3-\left (\frac {f'(x)}{f(x)}+f(x)\right ) \left (3 y'(x)+y(x)^2\right )+y''(x)+y(x) y'(x)-y(x)^3=0 \] Mathematica : cpu = 0.839201 (sec), leaf count = 0 , could not solve

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

Maple : cpu = 1.931 (sec), leaf count = 131

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