5.80   ODE No. 1528

$$\boxed{{\displaystyle \left(\frac{{\mathrm{d}}^3}{\mathrm{d}{x}^3}y\left(x\right)\right)\sin \left(x\right)+(2\cos \left(x\right)+1)\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)-\sin \left(x\right)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)-\cos \left(x\right)=0}}$$

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

Mathematica: cpu = 0.494563 (sec), leaf count = 72 $$\left\{\{y(x)\to \frac{\sin \left(\frac{x}{2}\right)(\sqrt{2}(c_{2}x\sin \left(\frac{x}{2}\right)+\cos \left(\frac{x}{2}\right)(c_2\log (2(\cos (x)+1))+2c_1))-2\cos \left(\frac{x}{2}\right){\sin }^{-1}(\cos (x)))}{\cos (x)-1}+c_3\}\right\}$$

Maple: cpu = 0.078 (sec), leaf count = 68 $$\{y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{1}}{-1+\cos \left(x\right)}(\ln (\sin \left(x\right))\sin \left(x\right)-\ln (-\frac{-1+\cos \left(x\right)}{\sin \left(x\right)})\sin \left(x\right)-\cos \left(x\right)x+x)+\mathit{\_}\mathit{C}\mathit{2}+\frac{\sin \left(x\right)\mathit{\_}\mathit{C}\mathit{3}}{-1+\cos \left(x\right)}+\frac{-\cos \left(x\right)x+\sin \left(x\right)-x}{\sin \left(x\right)}\}$$