2.1547   ODE No. 1547

1. Problem in Latex
2. Mathematica input
3. Maple input

$$3y(x)(2g(x)f^{\prime }(x)+5f(x)g^{\prime }(x)+6f(x{)}^{2}g(x)+g^{″}(x)+3g(x{)}^2)+y^{″}(x)(4f^{\prime }(x)+11f(x{)}^2+10g(x))+y^{\prime }(x)(f^{″}(x)+7f(x)f^{\prime }(x)+30f(x)g(x)+6f(x{)}^3+10g^{\prime }(x))+6f(x)y^{(3)}(x)+y^{(4)}(x)=0$$ ✗ Mathematica : cpu = 0.0344159 (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 = 0.026 (sec), leaf count = 87

$$\{y\left(x\right)=\sum _{\mathit{\_}\mathit{a}=1}^4{\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}({\mathit{\_}\mathit{Z}}^4+6f{\mathit{\_}\mathit{Z}}^3+(11f^2+4\mathit{d}\mathit{f}+10g){\mathit{\_}\mathit{Z}}^2+(6f^3+7\mathit{d}\mathit{f}f+30fg+\mathit{d}\mathit{d}\mathit{f}+10\mathit{d}\mathit{g})\mathit{\_}\mathit{Z}+18f^{2}g+6\mathit{d}\mathit{f}g+15\mathit{d}\mathit{g}f+9g^2+3\mathit{d}\mathit{d}\mathit{g},\mathit{i}\mathit{n}\mathit{d}\mathit{e}\mathit{x}=\mathit{\_}\mathit{a})x}{\mathit{\_}\mathit{C}}_{\mathit{\_}\mathit{a}}\}$$