2.1821   ODE No. 1821

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

\[ \left (x^2+2 y(x)^2 y'(x)\right ) y''(x)+2 y(x) y'(x)^3+3 x y'(x)+y(x)=0 \] Mathematica : cpu = 42.3157 (sec), leaf count = 0 , could not solve

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

Maple : cpu = 3.185 (sec), leaf count = 54

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