2.152   ODE No. 152

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

$$(x^2+1)y^{\prime }(x)-x(x^2+1){\cos }^2(y(x))+x\sin (y(x))\cos (y(x))=0$$ ✓ Mathematica : cpu = 0.231516 (sec), leaf count = 40

$$\left\{\{y(x)\to {\tan }^{-1}\left(\frac{-6c_1\sqrt{x^2+1}+x^4+2x^2+1}{3(x^2+1)}\right)\}\right\}$$

✓ Maple : cpu = 0.782 (sec), leaf count = 25

$$\{y\left(x\right)=\arctan \left(\frac{1}{3}({(x^2+1)}^{\frac{3}{2}}+3\mathit{\_}\mathit{C}\mathit{1})\frac{1}{\sqrt{x^2+1}}\right)\}$$