\[ 3 y(x) \left (2 g(x) f'(x)+5 f(x) g'(x)+6 f(x)^2 g(x)+g''(x)+3 g(x)^2\right )+y''(x) \left (4 f'(x)+11 f(x)^2+10 g(x)\right )+y'(x) \left (f''(x)+7 f(x) f'(x)+30 f(x) g(x)+6 f(x)^3+10 g'(x)\right )+6 f(x) y^{(3)}(x)+y^{(4)}(x)=0 \] ✗ Mathematica : cpu = 0.242293 (sec), leaf count = 0
, could not solve
DSolve[Derivative[1][y][x]*(6*f[x]^3 + 30*f[x]*g[x] + 7*f[x]*Derivative[1][f][x] + 10*Derivative[1][g][x] + Derivative[2][f][x]) + 3*y[x]*(6*f[x]^2*g[x] + 3*g[x]^2 + 2*g[x]*Derivative[1][f][x] + 5*f[x]*Derivative[1][g][x] + Derivative[2][g][x]) + (11*f[x]^2 + 10*g[x] + 4*Derivative[1][f][x])*Derivative[2][y][x] + 6*f[x]*Derivative[3][y][x] + Derivative[4][y][x] == 0, y[x], x]
✓ Maple : cpu = 0.02 (sec), leaf count = 87
\[y \relax (x ) = \moverset {4}{\munderset {\textit {\_a} =1}{\sum }}{\mathrm e}^{\RootOf \left (\textit {\_Z}^{4}+6 f \,\textit {\_Z}^{3}+\left (11 f^{2}+4 \mathit {df} +10 g \right ) \textit {\_Z}^{2}+\left (6 f^{3}+7 \mathit {df} f +30 f g +\mathit {ddf} +10 \mathit {dg} \right ) \textit {\_Z} +18 f^{2} g +6 \mathit {df} g +15 \mathit {dg} f +9 g^{2}+3 \mathit {ddg} , \mathit {index} =\textit {\_a} \right ) x} \textit {\_C}_{\textit {\_a}}\]