\[ x y(x) \left (a-2 x^2 y(x)^2+3 x y(x)\right )+b+2 x^3 y''(x)+x^2 (2 x y(x)+9) y'(x)=0 \] ✗ Mathematica : cpu = 40.1381 (sec), leaf count = 0
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]
, 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 = 0. (sec), leaf count = 0
dsolve(2*x^3*diff(diff(y(x),x),x)+x^2*(9+2*x*y(x))*diff(y(x),x)+b+x*y(x)*(a+3*x*y(x)-2*y(x)^2*x^2)=0,y(x))
, result contains DESol or ODESolStruc
\[y \left (x \right ) = \left (\textit {\_a} \,{\mathrm e}^{\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} +c_{1}}\right )\:\& \text {where}\:\left [\left \{\frac {d}{d \textit {\_a}}\textit {\_}b\left (\textit {\_a} \right )=\left (-\textit {\_a}^{3}+\frac {1}{2} \textit {\_a}^{2}+\frac {1}{2} \textit {\_a} a -\frac {5}{2} \textit {\_a} +\frac {1}{2} b \right ) \textit {\_}b\left (\textit {\_a} \right )^{3}+\left (-\textit {\_a} -\frac {3}{2}\right ) \textit {\_}b\left (\textit {\_a} \right )^{2}\right \}, \left \{\textit {\_a} =x y \left (x \right ), \textit {\_}b\left (\textit {\_a} \right )=-\frac {1}{x \left (x \left (\frac {d}{d x}y \left (x \right )\right )+y \left (x \right )\right )}\right \}, \left \{x ={\mathrm e}^{\int -\textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} -c_{1}}, y \left (x \right )=\textit {\_a} \,{\mathrm e}^{\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} +c_{1}}\right \}\right ]\]