3.21   ODE No. 21

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

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

Mathematica: cpu = 7.447446 (sec), leaf count = 69 $$\left\{\{y(x)\to -\frac{c_1(1-\sin (x)e^{\cos (x)}({\int }_1^x{e}^{-\cos (K[1])}dK[1]))-\sin (x)e^{\cos (x)}}{c_1{e}^{\cos (x)}{\int }_1^x{e}^{-\cos (K[1])}dK[1]+e^{\cos (x)}}\}\right\}$$

Maple: cpu = 0.093 (sec), leaf count = 25 $$\{y\left(x\right)=-\frac{{\mathrm{e}}^{-\cos \left(x\right)}}{\mathit{\_}\mathit{C}\mathit{1}+\int {\mathrm{e}}^{-\cos \left(x\right)}\mathrm{d}x}+\sin \left(x\right)\}$$

Sage: cpu = 3.404 (sec), leaf count = 0 $$[[y\left(x\right)=\frac{c{e}^{\cos \left(x\right)}\sin \left(x\right)+e^{\cos \left(x\right)}\int e^{(-\cos \left(x\right))}dx\sin \left(x\right)-1}{c{e}^{\cos \left(x\right)}+e^{\cos \left(x\right)}\int e^{(-\cos \left(x\right))}dx}],\mathtt{\text{riccati}}]$$