4.23.49 $(y^{\prime }(x{)}^2+1)(ax+{\tan }^{-1}(y^{\prime }(x)))+y^{\prime }(x)=0$

ODE
$$(y^{\prime }(x{)}^2+1)(ax+{\tan }^{-1}(y^{\prime }(x)))+y^{\prime }(x)=0$$ ODE Classification

[_quadrature]

Book solution method
Missing Variables ODE, Dependent variable missing, Solve for $x$

Mathematica ✗
cpu = 0.105349 (sec), leaf count = 0 , could not solve

DSolve[Derivative[1][y][x] + (a*x + ArcTan[Derivative[1][y][x]])*(1 + Derivative[1][y][x]^2) == 0, y[x], x]

Maple ✓
cpu = 0.074 (sec), leaf count = 30

$$\{y\left(x\right)=\int \tan \left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(ax{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2+{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2\mathit{\_}\mathit{Z}+ax+\tan \left(\mathit{\_}\mathit{Z}\right)+\mathit{\_}\mathit{Z})\right)\mathrm{d}x+\mathit{\_}\mathit{C}\mathit{1}\}$$ Mathematica raw input

DSolve[y'[x] + (a*x + ArcTan[y'[x]])*(1 + y'[x]^2) == 0,y[x],x]

Mathematica raw output

DSolve[Derivative[1][y][x] + (a*x + ArcTan[Derivative[1][y][x]])*(1 + Derivative
[1][y][x]^2) == 0, y[x], x]

Maple raw input

dsolve((1+diff(y(x),x)^2)*(arctan(diff(y(x),x))+a*x)+diff(y(x),x) = 0, y(x),'implicit')

Maple raw output

y(x) = Int(tan(RootOf(a*x*tan(_Z)^2+tan(_Z)^2*_Z+a*x+tan(_Z)+_Z)),x)+_C1