6.14   ODE No. 1547

$$\boxed{{\displaystyle \mathit{d}\mathit{4}\mathit{y}\left(x\right)+6f\frac{{\mathrm{d}}^3}{\mathrm{d}{x}^3}y\left(x\right)+(11f^2+4\mathit{d}\mathit{f}+10g)\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+(6f^3+7\mathit{d}\mathit{f}f+30fg+\mathit{d}\mathit{d}\mathit{f}+10\mathit{d}\mathit{g})\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+3(6f^{2}g+2\mathit{d}\mathit{f}g+5\mathit{d}\mathit{g}f+3g^2+\mathit{d}\mathit{d}\mathit{g})y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.034504 (sec), leaf count = 116 $$\text{DSolve}[3y(x)(2g(x)f^{\prime }(x)+5f(x)g^{\prime }(x)+6f(x{)}^{2}g(x)+g^{″}(x)+3g(x{)}^2)+y^{″}(x)(4f^{\prime }(x)+11f(x{)}^2+10g(x))+y^{\prime }(x)(f^{″}(x)+7f(x)f^{\prime }(x)+30f(x)g(x)+6f(x{)}^3+10g^{\prime }(x))+6f(x)y^{(3)}(x)+y^{(4)}(x)=0,y(x),x]$$

Maple: cpu = 0.015 (sec), leaf count = 87 $$\{y\left(x\right)=\sum _{\mathit{\_}\mathit{a}=1}^4{\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}({\mathit{\_}\mathit{Z}}^4+6f{\mathit{\_}\mathit{Z}}^3+(11f^2+4\mathit{d}\mathit{f}+10g){\mathit{\_}\mathit{Z}}^2+(6f^3+7\mathit{d}\mathit{f}f+30fg+\mathit{d}\mathit{d}\mathit{f}+10\mathit{d}\mathit{g})\mathit{\_}\mathit{Z}+18f^{2}g+6\mathit{d}\mathit{f}g+15\mathit{d}\mathit{g}f+9g^2+3\mathit{d}\mathit{d}\mathit{g},\mathit{i}\mathit{n}\mathit{d}\mathit{e}\mathit{x}=\mathit{\_}\mathit{a})x}{\mathit{\_}\mathit{C}}_{\mathit{\_}\mathit{a}}\}$$