\[ A(x) \left (f(x) y''(x)+g(x) y'(x)+h(x) y(x)\right )+f'(x) y''(x)+f(x) y^{(3)}(x)+g'(x) y'(x)+g(x) y''(x)+y(x) h'(x)+h(x) y'(x)=0 \] ✗ Mathematica : cpu = 0.0241145 (sec), leaf count = 0
, could not solve
DSolve[y[x]*Derivative[1][h][x] + h[x]*Derivative[1][y][x] + Derivative[1][g][x]*Derivative[1][y][x] + g[x]*Derivative[2][y][x] + Derivative[1][f][x]*Derivative[2][y][x] + A[x]*(h[x]*y[x] + g[x]*Derivative[1][y][x] + f[x]*Derivative[2][y][x]) + f[x]*Derivative[3][y][x] == 0, y[x], x]
✗ Maple : cpu = 0. (sec), leaf count = 0
, result contains DESol or ODESolStruc
\[y \relax (x ) = \mathit {DESol}\left (\left \{f \relax (x ) \left (\frac {d^{3}}{d x^{3}}\textit {\_Y} \relax (x )\right )+\left (\frac {d}{d x}f \relax (x )+g \relax (x )+A \relax (x ) f \relax (x )\right ) \left (\frac {d^{2}}{d x^{2}}\textit {\_Y} \relax (x )\right )+\left (\frac {d}{d x}g \relax (x )+h \relax (x )+A \relax (x ) g \relax (x )\right ) \left (\frac {d}{d x}\textit {\_Y} \relax (x )\right )+\left (\frac {d}{d x}h \relax (x )+A \relax (x ) h \relax (x )\right ) \textit {\_Y} \relax (x )\right \}, \left \{\textit {\_Y} \relax (x )\right \}\right )\]