2.1575   ODE No. 1575

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

$$-f(x)+y^{(4)}(x){\sin }^6(x)+4y^{(3)}(x){\sin }^5(x)\cos (x)-6{\sin }^6(x)y^{″}(x)-4{\sin }^5(x)\cos (x)y^{\prime }(x)+y(x){\sin }^6(x)=0$$ ✗ Mathematica : cpu = 0.0654131 (sec), leaf count = 0 , could not solve

DSolve[-f[x] + Sin[x]^6*y[x] - 4*Cos[x]*Sin[x]^5*Derivative[1][y][x] - 6*Sin[x]^6*Derivative[2][y][x] + 4*Cos[x]*Sin[x]^5*Derivative[3][y][x] + Sin[x]^6*Derivative[4][y][x] == 0, y[x], x]

✓ Maple : cpu = 0.399 (sec), leaf count = 1277

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