\[ a y(x) y''(x)+y^{(3)}(x)=0 \] ✗ Mathematica : cpu = 0.0290372 (sec), leaf count = 0
DSolve[a*y[x]*Derivative[2][y][x] + Derivative[3][y][x] == 0,y[x],x]
, could not solve
DSolve[a*y[x]*Derivative[2][y][x] + Derivative[3][y][x] == 0, y[x], x]
✗ Maple : cpu = 0. (sec), leaf count = 0
dsolve(diff(diff(diff(y(x),x),x),x)+a*y(x)*diff(diff(y(x),x),x)=0,y(x))
, result contains DESol or ODESolStruc
\[y \left (x \right ) = \left ({\mathrm e}^{\int \textit {\_g} \left (\textit {\_f} \right )d \textit {\_f} +c_{2}}\right )\boldsymbol {\mathrm {where}}\left [\left \{\frac {d}{d \textit {\_f}}\textit {\_g} \left (\textit {\_f} \right )=\left (6 \textit {\_f} +2 a \right ) \textit {\_g} \left (\textit {\_f} \right )^{3}+\frac {\left (7 \textit {\_f} +a \right ) \textit {\_g} \left (\textit {\_f} \right )^{2}}{\textit {\_f}}+\frac {\textit {\_g} \left (\textit {\_f} \right )}{\textit {\_f}}\right \}, \left \{\textit {\_f} =\frac {\frac {d}{d x}y \left (x \right )}{y \left (x \right )^{2}}, \textit {\_g} \left (\textit {\_f} \right )=-\frac {y \left (x \right )^{2}}{-\frac {y \left (x \right ) \left (\frac {d^{2}}{d x^{2}}y \left (x \right )\right )}{\frac {d}{d x}y \left (x \right )}+2 \frac {d}{d x}y \left (x \right )}\right \}, \left \{x =\int \frac {{\mathrm e}^{\int -\textit {\_g} \left (\textit {\_f} \right )d \textit {\_f} -c_{2}} \textit {\_g} \left (\textit {\_f} \right )}{\textit {\_f}}d \textit {\_f} +c_{1}, y \left (x \right )={\mathrm e}^{\int \textit {\_g} \left (\textit {\_f} \right )d \textit {\_f} +c_{2}}\right \}\right ]\]