4.13.23 $y^{\prime }(x)(a+b+y(x)+x{)}^2=2(a+y(x){)}^2$

ODE
$$y^{\prime }(x)(a+b+y(x)+x{)}^2=2(a+y(x){)}^2$$ ODE Classification

[[_homogeneous, `class C`], _rational]

Book solution method
Equation linear in the variables, $y^{\prime }(x)=f\left(\frac{X_1}{X_2}\right)$

Mathematica ✓
cpu = 0.0873864 (sec), leaf count = 25

$$\text{Solve}[2{\tan }^{-1}\left(\frac{b+x}{a+y(x)}\right)+c_1=\log (a+y(x)),y(x)]$$

Maple ✓
cpu = 0.028 (sec), leaf count = 47

$$\{2\arctan \left(\frac{-a-y\left(x\right)}{b+x}\right)-\ln \left(\frac{-a-y\left(x\right)}{b+x}\right)-\ln (b+x)-\mathit{\_}\mathit{C}\mathit{1}=0\}$$ Mathematica raw input

DSolve[(a + b + x + y[x])^2*y'[x] == 2*(a + y[x])^2,y[x],x]

Mathematica raw output

Solve[2*ArcTan[(b + x)/(a + y[x])] + C[1] == Log[a + y[x]], y[x]]

Maple raw input

dsolve((a+b+x+y(x))^2*diff(y(x),x) = 2*(a+y(x))^2, y(x),'implicit')

Maple raw output

2*arctan((-a-y(x))/(b+x))-ln((-a-y(x))/(b+x))-ln(b+x)-_C1 = 0