\[ y(x) \left (f(x) g(x)+g'(x)\right )+f(x) y''(x)+g(x) y'(x)+y^{(3)}(x)=0 \] ✗ Mathematica : cpu = 0.0106054 (sec), leaf count = 0
DSolve[y[x]*(f[x]*g[x] + Derivative[1][g][x]) + g[x]*Derivative[1][y][x] + f[x]*Derivative[2][y][x] + Derivative[3][y][x] == 0,y[x],x]
, could not solve
DSolve[y[x]*(f[x]*g[x] + Derivative[1][g][x]) + g[x]*Derivative[1][y][x] + f[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)+f(x)*diff(diff(y(x),x),x)+g(x)*diff(y(x),x)+(f(x)*g(x)+diff(g(x),x))*y(x)=0,y(x))
, result contains DESol or ODESolStruc
\[y \left (x \right ) = \mathit {DESol}\left (\left \{\frac {d^{3}}{d x^{3}}\textit {\_Y} \left (x \right )+f \left (x \right ) \left (\frac {d^{2}}{d x^{2}}\textit {\_Y} \left (x \right )\right )+g \left (x \right ) \left (\frac {d}{d x}\textit {\_Y} \left (x \right )\right )+\left (f \left (x \right ) g \left (x \right )+\frac {d}{d x}g \left (x \right )\right ) \textit {\_Y} \left (x \right )\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )\]