ODE No. 1821

\[ \left (x^2+2 y(x)^2 y'(x)\right ) y''(x)+2 y(x) y'(x)^3+3 x y'(x)+y(x)=0 \] Mathematica : cpu = 41.8143 (sec), leaf count = 0

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]
 

, 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 = 0. (sec), leaf count = 0

dsolve((2*y(x)^2*diff(y(x),x)+x^2)*diff(diff(y(x),x),x)+2*y(x)*diff(y(x),x)^3+3*x*diff(y(x),x)+y(x)=0,y(x))
 

, result contains DESol or ODESolStruc

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