7.2   ODE No. 1575

$$\boxed{{\displaystyle \mathit{d}\mathit{4}\mathit{y}\left(x\right){(\sin \left(x\right))}^6+4\left(\frac{{\mathrm{d}}^3}{\mathrm{d}{x}^3}y\left(x\right)\right){(\sin \left(x\right))}^5\cos \left(x\right)-6\left(\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)\right){(\sin \left(x\right))}^6-4\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right){(\sin \left(x\right))}^5\cos \left(x\right)+y\left(x\right){(\sin \left(x\right))}^6-f=0}}$$

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

Mathematica: cpu = 0.067008 (sec), leaf count = 61 $$\text{DSolve}[-f(x)+y^{(4)}(x){\sin }^6(x)+4y^{(3)}(x){\sin }^5(x)\cos (x)-6{\sin }^6(x)y^{″}(x)-4{\sin }^5(x)\cos (x)y^{\prime }(x)+y(x){\sin }^6(x)=0,y(x),x]$$

Maple: cpu = 0.265 (sec), leaf count = 1277 $$\{y\left(x\right)=-\frac{f(-12\cos \left(x\right){(\sin \left(x\right))}^2{\mathrm{e}}^{6ix}{x}^3+80{(\sin \left(x\right))}^4\ln (1+{\mathrm{e}}^{ix}){\mathrm{e}}^{6ix}x-80{(\sin \left(x\right))}^4\ln (1-{\mathrm{e}}^{ix}){\mathrm{e}}^{6ix}x+18\cos \left(x\right){(\sin \left(x\right))}^2{\mathrm{e}}^{4ix}{x}^3-12{(\sin \left(x\right))}^4\ln (1-{\mathrm{e}}^{ix}){\mathrm{e}}^{6ix}{x}^3+12{(\sin \left(x\right))}^4{\mathrm{e}}^{6ix}\ln (\csc \left(x\right)-\cot \left(x\right))x^3+3\cos \left(x\right){(\sin \left(x\right))}^2{\mathrm{e}}^{8ix}{x}^3-20{(\sin \left(x\right))}^4\ln (1+{\mathrm{e}}^{ix}){\mathrm{e}}^{8ix}x-18{(\sin \left(x\right))}^4\ln (1+{\mathrm{e}}^{ix}){\mathrm{e}}^{4ix}{x}^3+20{(\sin \left(x\right))}^4\ln (1-{\mathrm{e}}^{ix}){\mathrm{e}}^{8ix}x+18{(\sin \left(x\right))}^4\ln (1-{\mathrm{e}}^{ix}){\mathrm{e}}^{4ix}{x}^3-18{(\sin \left(x\right))}^4{\mathrm{e}}^{4ix}\ln (\csc \left(x\right)-\cot \left(x\right))x^3-3{(\sin \left(x\right))}^4\ln (1+{\mathrm{e}}^{ix}){\mathrm{e}}^{8ix}{x}^3+3{(\sin \left(x\right))}^4\ln (1-{\mathrm{e}}^{ix}){\mathrm{e}}^{8ix}{x}^3-3{(\sin \left(x\right))}^4{\mathrm{e}}^{8ix}\ln (\csc \left(x\right)-\cot \left(x\right))x^3+12{(\sin \left(x\right))}^4\ln (1+{\mathrm{e}}^{ix}){\mathrm{e}}^{6ix}{x}^3+2x^3\cos \left(x\right)+2\cos \left(x\right){\mathrm{e}}^{8ix}{x}^3-120{(\sin \left(x\right))}^4\ln (1+{\mathrm{e}}^{ix}){\mathrm{e}}^{4ix}x+120{(\sin \left(x\right))}^4\ln (1-{\mathrm{e}}^{ix}){\mathrm{e}}^{4ix}x+18i{(\sin \left(x\right))}^4\mathit{p}\mathit{o}\mathit{l}\mathit{y}\mathit{l}\mathit{o}\mathit{g}(4,{\mathrm{e}}^{ix}){\mathrm{e}}^{8ix}+20i{(\sin \left(x\right))}^4\mathit{p}\mathit{o}\mathit{l}\mathit{y}\mathit{l}\mathit{o}\mathit{g}(2,-{\mathrm{e}}^{ix}){\mathrm{e}}^{8ix}-18i{(\sin \left(x\right))}^4\mathit{p}\mathit{o}\mathit{l}\mathit{y}\mathit{l}\mathit{o}\mathit{g}(4,-{\mathrm{e}}^{ix}){\mathrm{e}}^{8ix}-20i{(\sin \left(x\right))}^4\mathit{p}\mathit{o}\mathit{l}\mathit{y}\mathit{l}\mathit{o}\mathit{g}(2,{\mathrm{e}}^{ix}){\mathrm{e}}^{8ix}-72i{(\sin \left(x\right))}^4\mathit{p}\mathit{o}\mathit{l}\mathit{y}\mathit{l}\mathit{o}\mathit{g}(4,{\mathrm{e}}^{ix}){\mathrm{e}}^{6ix}-80i{(\sin \left(x\right))}^4\mathit{p}\mathit{o}\mathit{l}\mathit{y}\mathit{l}\mathit{o}\mathit{g}(2,-{\mathrm{e}}^{ix}){\mathrm{e}}^{6ix}+72i{(\sin \left(x\right))}^4\mathit{p}\mathit{o}\mathit{l}\mathit{y}\mathit{l}\mathit{o}\mathit{g}(4,-{\mathrm{e}}^{ix}){\mathrm{e}}^{6ix}+80i{(\sin \left(x\right))}^4\mathit{p}\mathit{o}\mathit{l}\mathit{y}\mathit{l}\mathit{o}\mathit{g}(2,{\mathrm{e}}^{ix}){\mathrm{e}}^{6ix}+108i{(\sin \left(x\right))}^4\mathit{p}\mathit{o}\mathit{l}\mathit{y}\mathit{l}\mathit{o}\mathit{g}(4,{\mathrm{e}}^{ix}){\mathrm{e}}^{4ix}+120i{(\sin \left(x\right))}^4\mathit{p}\mathit{o}\mathit{l}\mathit{y}\mathit{l}\mathit{o}\mathit{g}(2,-{\mathrm{e}}^{ix}){\mathrm{e}}^{4ix}-108i{(\sin \left(x\right))}^4\mathit{p}\mathit{o}\mathit{l}\mathit{y}\mathit{l}\mathit{o}\mathit{g}(4,-{\mathrm{e}}^{ix}){\mathrm{e}}^{4ix}-120i{(\sin \left(x\right))}^4\mathit{p}\mathit{o}\mathit{l}\mathit{y}\mathit{l}\mathit{o}\mathit{g}(2,{\mathrm{e}}^{ix}){\mathrm{e}}^{4ix}-3{(\sin \left(x\right))}^4\ln (1+{\mathrm{e}}^{ix})x^3+3{(\sin \left(x\right))}^4\ln (1-{\mathrm{e}}^{ix})x^3+6{(\sin \left(x\right))}^4{\mathrm{e}}^{7ix}{x}^3-22{(\sin \left(x\right))}^4{\mathrm{e}}^{5ix}{x}^3+6{(\sin \left(x\right))}^4{\mathrm{e}}^{ix}{x}^3-22{(\sin \left(x\right))}^4{\mathrm{e}}^{3ix}{x}^3-3{(\sin \left(x\right))}^4\ln (\csc \left(x\right)-\cot \left(x\right))x^3+3x^3\cos \left(x\right){(\sin \left(x\right))}^2-20{(\sin \left(x\right))}^4\ln (1+{\mathrm{e}}^{ix})x+20{(\sin \left(x\right))}^4\ln (1-{\mathrm{e}}^{ix})x-8\cos \left(x\right){\mathrm{e}}^{2ix}{x}^3+18i{(\sin \left(x\right))}^4\mathit{p}\mathit{o}\mathit{l}\mathit{y}\mathit{l}\mathit{o}\mathit{g}(4,{\mathrm{e}}^{ix})+20i{(\sin \left(x\right))}^4\mathit{p}\mathit{o}\mathit{l}\mathit{y}\mathit{l}\mathit{o}\mathit{g}(2,-{\mathrm{e}}^{ix})-18i{(\sin \left(x\right))}^4\mathit{p}\mathit{o}\mathit{l}\mathit{y}\mathit{l}\mathit{o}\mathit{g}(4,-{\mathrm{e}}^{ix})-20i{(\sin \left(x\right))}^4\mathit{p}\mathit{o}\mathit{l}\mathit{y}\mathit{l}\mathit{o}\mathit{g}(2,{\mathrm{e}}^{ix})-4i{(\sin \left(x\right))}^4{\mathrm{e}}^{7ix}+12i{(\sin \left(x\right))}^4{\mathrm{e}}^{5ix}+4i{(\sin \left(x\right))}^4{\mathrm{e}}^{ix}-12i{(\sin \left(x\right))}^4{\mathrm{e}}^{3ix}+12{(\sin \left(x\right))}^4\ln (1+{\mathrm{e}}^{ix}){\mathrm{e}}^{2ix}{x}^3-12{(\sin \left(x\right))}^4\ln (1-{\mathrm{e}}^{ix}){\mathrm{e}}^{2ix}{x}^3+12{(\sin \left(x\right))}^4{\mathrm{e}}^{2ix}\ln (\csc \left(x\right)-\cot \left(x\right))x^3-12\cos \left(x\right){(\sin \left(x\right))}^2{\mathrm{e}}^{2ix}{x}^3+80{(\sin \left(x\right))}^4\ln (1+{\mathrm{e}}^{ix}){\mathrm{e}}^{2ix}x-80{(\sin \left(x\right))}^4\ln (1-{\mathrm{e}}^{ix}){\mathrm{e}}^{2ix}x-72i{(\sin \left(x\right))}^4\mathit{p}\mathit{o}\mathit{l}\mathit{y}\mathit{l}\mathit{o}\mathit{g}(4,{\mathrm{e}}^{ix}){\mathrm{e}}^{2ix}-80i{(\sin \left(x\right))}^4\mathit{p}\mathit{o}\mathit{l}\mathit{y}\mathit{l}\mathit{o}\mathit{g}(2,-{\mathrm{e}}^{ix}){\mathrm{e}}^{2ix}+72i{(\sin \left(x\right))}^4\mathit{p}\mathit{o}\mathit{l}\mathit{y}\mathit{l}\mathit{o}\mathit{g}(4,-{\mathrm{e}}^{ix}){\mathrm{e}}^{2ix}+80i{(\sin \left(x\right))}^4\mathit{p}\mathit{o}\mathit{l}\mathit{y}\mathit{l}\mathit{o}\mathit{g}(2,{\mathrm{e}}^{ix}){\mathrm{e}}^{2ix}-8\cos \left(x\right){\mathrm{e}}^{6ix}{x}^3+12\cos \left(x\right){\mathrm{e}}^{4ix}{x}^3-160{(\sin \left(x\right))}^4\mathit{A}\mathit{r}\mathit{t}\mathit{a}\mathit{n}\mathit{h}\left({\mathrm{e}}^{ix}\right){\mathrm{e}}^{6ix}x+240{(\sin \left(x\right))}^4\mathit{A}\mathit{r}\mathit{t}\mathit{a}\mathit{n}\mathit{h}\left({\mathrm{e}}^{ix}\right){\mathrm{e}}^{4ix}x+40{(\sin \left(x\right))}^4\mathit{A}\mathit{r}\mathit{t}\mathit{a}\mathit{n}\mathit{h}\left({\mathrm{e}}^{ix}\right){\mathrm{e}}^{8ix}x-160{(\sin \left(x\right))}^4\mathit{A}\mathit{r}\mathit{t}\mathit{a}\mathit{n}\mathit{h}\left({\mathrm{e}}^{ix}\right){\mathrm{e}}^{2ix}x+40{(\sin \left(x\right))}^4\mathit{A}\mathit{r}\mathit{t}\mathit{a}\mathit{n}\mathit{h}\left({\mathrm{e}}^{ix}\right)x)}{48{({\mathrm{e}}^{2ix}-1)}^4{(\sin \left(x\right))}^5}+\frac{\mathit{\_}\mathit{C}\mathit{1}}{\sin \left(x\right)}+\frac{\mathit{\_}\mathit{C}\mathit{2}x}{\sin \left(x\right)}+\frac{\mathit{\_}\mathit{C}\mathit{3}{x}^2}{\sin \left(x\right)}+\frac{\mathit{\_}\mathit{C}\mathit{4}{x}^3}{\sin \left(x\right)}\}$$