2.1547   ODE No. 1547

\[ 3 y(x) \left (2 g(x) f'(x)+5 f(x) g'(x)+6 f(x)^2 g(x)+g''(x)+3 g(x)^2\right )+y''(x) \left (4 f'(x)+11 f(x)^2+10 g(x)\right )+y'(x) \left (f''(x)+7 f(x) f'(x)+30 f(x) g(x)+6 f(x)^3+10 g'(x)\right )+6 f(x) y^{(3)}(x)+y^{(4)}(x)=0 \]

✗ Mathematica : cpu = 0.19127 (sec), leaf count = 0

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]
 

, 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 = 0.017 (sec), leaf count = 87

dsolve(diff(diff(diff(diff(y(x),x),x),x),x)+6*f*diff(diff(diff(y(x),x),x),x)+(11*f^2+4*df+10*g)*diff(diff(y(x),x),x)+(6*f^3+7*df*f+30*f*g+ddf+10*dg)*diff(y(x),x)+3*(6*f^2*g+2*df*g+5*dg*f+3*g^2+ddg)*y(x)=0,y(x))
 

\[y \left (x \right ) = \moverset {4}{\munderset {\textit {\_a} =1}{\sum }}{\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}+6 f \,\textit {\_Z}^{3}+\left (11 f^{2}+4 \operatorname {df} +10 g \right ) \textit {\_Z}^{2}+\left (6 f^{3}+7 \operatorname {df} f +30 f g +\operatorname {ddf} +10 \operatorname {dg} \right ) \textit {\_Z} +18 f^{2} g +6 \operatorname {df} g +15 \operatorname {dg} f +9 g^{2}+3 \operatorname {ddg} , \operatorname {index} =\textit {\_a} \right ) x} \textit {\_C}_{\textit {\_a}}\]