ODE No. 152

$$(x^2+1)y^{\prime }(x)-x(x^2+1){\cos }^2(y(x))+x\sin (y(x))\cos (y(x))=0$$ ✓ Mathematica : cpu = 0.387859 (sec), leaf count = 40

DSolve[-(x*(1 + x^2)*Cos[y[x]]^2) + x*Cos[y[x]]*Sin[y[x]] + (1 + x^2)*Derivative[1][y][x] == 0,y[x],x]
 

$$\left\{\{y(x)\to {\tan }^{-1}\left(\frac{x^4+2x^2-6c_1\sqrt{x^2+1}+1}{3(x^2+1)}\right)\}\right\}$$ ✓ Maple : cpu = 0.904 (sec), leaf count = 159

dsolve((x^2+1)*diff(y(x),x)+x*sin(y(x))*cos(y(x))-x*(x^2+1)*cos(y(x))^2 = 0,y(x))
 

$$y\left(x\right)=\frac{\arctan (\frac{6\sqrt{x^2+1}(x^2\sqrt{x^2+1}+\sqrt{x^2+1}+3c_1)}{(6x^2{c}_1+6c_1)\sqrt{x^2+1}+x^6+3x^4+12x^2+9c_1^2+10},\frac{(-6x^2{c}_1-6c_1)\sqrt{x^2+1}-x^6-3x^4+6x^2-9c_1^2+8}{(6x^2{c}_1+6c_1)\sqrt{x^2+1}+x^6+3x^4+12x^2+9c_1^2+10})}{2}$$