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 = 0.0691642 (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 = 0.508 (sec), leaf count = 638

$$\{y\left(x\right)=\frac{1}{48{({\mathrm{e}}^{2ix}-1)}^4\sin \left(x\right)}(12f({\mathrm{e}}^{2ix}-3/2{\mathrm{e}}^{4ix}+{\mathrm{e}}^{6ix}-1/4{\mathrm{e}}^{8ix}-1/4)(x^2+\frac{20}{3})x\ln (1-{\mathrm{e}}^{ix})+80if({\mathrm{e}}^{2ix}-\frac{3{\mathrm{e}}^{4ix}}{2}+{\mathrm{e}}^{6ix}-\frac{{\mathrm{e}}^{8ix}}{4}-\frac{1}{4})\mathit{p}\mathit{o}\mathit{l}\mathit{y}\mathit{l}\mathit{o}\mathit{g}(2,-{\mathrm{e}}^{ix})+72if({\mathrm{e}}^{2ix}-\frac{3{\mathrm{e}}^{4ix}}{2}+{\mathrm{e}}^{6ix}-\frac{{\mathrm{e}}^{8ix}}{4}-\frac{1}{4})\mathit{p}\mathit{o}\mathit{l}\mathit{y}\mathit{l}\mathit{o}\mathit{g}(4,{\mathrm{e}}^{ix})-12f({\mathrm{e}}^{2ix}-3/2{\mathrm{e}}^{4ix}+{\mathrm{e}}^{6ix}-1/4{\mathrm{e}}^{8ix}-1/4)x^3\ln (\csc \left(x\right)-\cot \left(x\right))-12f({\mathrm{e}}^{2ix}-3/2{\mathrm{e}}^{4ix}+{\mathrm{e}}^{6ix}-1/4{\mathrm{e}}^{8ix}-1/4)(x^2+\frac{20}{3})x\ln ({\mathrm{e}}^{ix}+1)-80if({\mathrm{e}}^{2ix}-\frac{3{\mathrm{e}}^{4ix}}{2}+{\mathrm{e}}^{6ix}-\frac{{\mathrm{e}}^{8ix}}{4}-\frac{1}{4})\mathit{p}\mathit{o}\mathit{l}\mathit{y}\mathit{l}\mathit{o}\mathit{g}(2,{\mathrm{e}}^{ix})-72if({\mathrm{e}}^{2ix}-\frac{3{\mathrm{e}}^{4ix}}{2}+{\mathrm{e}}^{6ix}-\frac{{\mathrm{e}}^{8ix}}{4}-\frac{1}{4})\mathit{p}\mathit{o}\mathit{l}\mathit{y}\mathit{l}\mathit{o}\mathit{g}(4,-{\mathrm{e}}^{ix})+(48\mathit{\_}\mathit{C}\mathit{4}{x}^3+48\mathit{\_}\mathit{C}\mathit{3}{x}^2+48\mathit{\_}\mathit{C}\mathit{2}x+48\mathit{\_}\mathit{C}\mathit{1}){\left({\mathrm{e}}^{2ix}\right)}^4+(-192\mathit{\_}\mathit{C}\mathit{4}{x}^3-192\mathit{\_}\mathit{C}\mathit{3}{x}^2-192\mathit{\_}\mathit{C}\mathit{2}x-192\mathit{\_}\mathit{C}\mathit{1}){\left({\mathrm{e}}^{2ix}\right)}^3+(288\mathit{\_}\mathit{C}\mathit{4}{x}^3+288\mathit{\_}\mathit{C}\mathit{3}{x}^2+288\mathit{\_}\mathit{C}\mathit{2}x+288\mathit{\_}\mathit{C}\mathit{1}){\left({\mathrm{e}}^{2ix}\right)}^2+(160\mathit{A}\mathit{r}\mathit{t}\mathit{a}\mathit{n}\mathit{h}\left({\mathrm{e}}^{ix}\right)fx+8f({(\csc \left(x\right))}^2+3/2)\csc \left(x\right)x^3\cot \left(x\right)-192\mathit{\_}\mathit{C}\mathit{4}{x}^3-192\mathit{\_}\mathit{C}\mathit{3}{x}^2-192\mathit{\_}\mathit{C}\mathit{2}x-192\mathit{\_}\mathit{C}\mathit{1}){\mathrm{e}}^{2ix}-240f(\mathit{A}\mathit{r}\mathit{t}\mathit{a}\mathit{n}\mathit{h}\left({\mathrm{e}}^{ix}\right)+1/20({(\csc \left(x\right))}^2+3/2)\csc \left(x\right)x^2\cot \left(x\right))x{\mathrm{e}}^{4ix}+160f(\mathit{A}\mathit{r}\mathit{t}\mathit{a}\mathit{n}\mathit{h}\left({\mathrm{e}}^{ix}\right)+1/20({(\csc \left(x\right))}^2+3/2)\csc \left(x\right)x^2\cot \left(x\right))x{\mathrm{e}}^{6ix}-40f(\mathit{A}\mathit{r}\mathit{t}\mathit{a}\mathit{n}\mathit{h}\left({\mathrm{e}}^{ix}\right)+1/20({(\csc \left(x\right))}^2+3/2)\csc \left(x\right)x^2\cot \left(x\right))x{\mathrm{e}}^{8ix}-40\mathit{A}\mathit{r}\mathit{t}\mathit{a}\mathit{n}\mathit{h}\left({\mathrm{e}}^{ix}\right)fx+12f(\frac{11x^3}{6}+i){\mathrm{e}}^{3ix}-12f(-\frac{11x^3}{6}+i){\mathrm{e}}^{5ix}+4f(-3/2x^3+i){\mathrm{e}}^{7ix}-4f(3/2x^3+i){\mathrm{e}}^{ix}-2f({(\csc \left(x\right))}^2+3/2)\csc \left(x\right)x^3\cot \left(x\right)+48\mathit{\_}\mathit{C}\mathit{4}{x}^3+48\mathit{\_}\mathit{C}\mathit{3}{x}^2+48\mathit{\_}\mathit{C}\mathit{2}x+48\mathit{\_}\mathit{C}\mathit{1})\}$$