\[ y'(x) \left (7 f(x) f'(x)+f''(x)+30 f(x) g(x)+6 f(x)^3+10 g'(x)\right )+3 y(x) \left (2 g(x) f'(x)+5 f(x) g'(x)+6 f(x)^2 g(x)+g''(x)+3 g(x)^2\right )+y''(x) \left (4 f'(x)+11 f(x)^2+10 g(x)\right )+6 f(x) y^{(3)}(x)+y^{(4)}(x)=0 \] ✗ Mathematica : cpu = 0.0263259 (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 = 0.013 (sec), leaf count = 87
\[ \left \{ y \left ( x \right ) =\sum _{{\it \_a}=1}^{4}{{\rm e}^{{\it RootOf} \left ( {{\it \_Z}}^{4}+6\,f{{\it \_Z}}^{3}+ \left ( 11\,{f}^{2}+4\,{\it df}+10\,g \right ) {{\it \_Z}}^{2}+ \left ( 6\,{f}^{3}+7\,{\it df}\,f+30\,fg+{\it ddf}+10\,{\it dg} \right ) {\it \_Z}+18\,{f}^{2}g+6\,{\it df}\,g+15\,{\it dg}\,f+9\,{g}^{2}+3\,{\it ddg},{\it index}={\it \_a} \right ) x}}{\it \_C}_{{{\it \_a}}} \right \} \]