2.1762   ODE No. 1762

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

\[ a y(x) y'(x)+b x y(x)^3+x y(x) y''(x)-x y'(x)^2=0 \] Mathematica : cpu = 50.1901 (sec), leaf count = 0 , could not solve

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

Maple : cpu = 2.309 (sec), leaf count = 108

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