2.80   ODE No. 80

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

$$(1-f^{\prime }(x))\cos (y(x))-f^{\prime }(x)+f(x)\sin (y(x))+y^{\prime }(x)-1=0$$ ✓ Mathematica : cpu = 0.0570775 (sec), leaf count = 72

$$\left\{\{y(x)\to 2{\tan }^{-1}(f(x)+\frac{1}{\exp ({\int }_1^x-f(K[1])dK[1]){\int }_1^x-\exp (-{\int }_1^{K[2]}-f(K[1])dK[1])dK[2]+c_1\exp ({\int }_1^x-f(K[1])dK[1])})\}\right\}$$ ✓ Maple : cpu = 1.051 (sec), leaf count = 41

$$\{y\left(x\right)=2\arctan \left(\frac{-{\mathrm{e}}^{\int f\left(x\right)\mathrm{d}x}+\int {\mathrm{e}}^{\int f\left(x\right)\mathrm{d}x}\mathrm{d}xf\left(x\right)+f\left(x\right)\mathit{\_}\mathit{C}\mathit{1}}{\mathit{\_}\mathit{C}\mathit{1}+\int {\mathrm{e}}^{\int f\left(x\right)\mathrm{d}x}\mathrm{d}x}\right)\}$$