\[ \boxed { {\it d4y} \left ( x \right ) +6\,f{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) + \left ( 11\,{f}^{2}+4\,{\it df}+10\,g \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( 6\,{f}^{3}+7\,{\it df}\,f+30\,fg+{\it ddf}+10\,{\it dg} \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +3\, \left ( 6\,{f}^{2}g+2\,{\it df}\,g+5\,{\it dg}\,f+3\,{g}^{2}+{\it ddg} \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.034504 (sec), leaf count = 116 \[ \text {DSolve}\left [3 y(x) \left (2 g(x) f'(x)+5 f(x) g'(x)+6 f(x)^2 g(x)+g''(x)+3 g(x)^2\right )+y''(x) \left (4 f'(x)+11 f(x)^2+10 g(x)\right )+y'(x) \left (f''(x)+7 f(x) f'(x)+30 f(x) g(x)+6 f(x)^3+10 g'(x)\right )+6 f(x) y^{(3)}(x)+y^{(4)}(x)=0,y(x),x\right ] \]
Maple: cpu = 0.015 (sec), leaf count = 87 \[ \left \{ y \left ( x \right ) =\sum _{{\it \_a}=1}^{4}{{\rm e}^{{\it RootOf} \left ( {{\it \_Z}}^{4}+6\,f{{\it \_Z}}^{3}+ \left ( 11\,{f}^{2} +4\,{\it df}+10\,g \right ) {{\it \_Z}}^{2}+ \left ( 6\,{f}^{3}+7\,{\it df}\,f+30\,fg+{\it ddf}+10\,{\it dg} \right ) {\it \_Z}+18\,{f}^{2}g+6 \,{\it df}\,g+15\,{\it dg}\,f+9\,{g}^{2}+3\,{\it ddg},{\it index}={ \it \_a} \right ) x}}{\it \_C}_{{{\it \_a}}} \right \} \]