ODE
\[ y'(x) (a+b+y(x)+x)^2=2 (a+y(x))^2 \] ODE Classification
[[_homogeneous, `class C`], _rational]
Book solution method
Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)
Mathematica ✓
cpu = 0.441219 (sec), leaf count = 25
\[\text {Solve}\left [2 \tan ^{-1}\left (\frac {b+x}{a+y(x)}\right )+c_1=\log (a+y(x)),y(x)\right ]\]
Maple ✓
cpu = 0.101 (sec), leaf count = 27
\[[y \left (x \right ) = -a -\tan \left (\RootOf \left (-2 \textit {\_Z} +\ln \left (\tan \left (\textit {\_Z} \right )\right )+\ln \left (b +x \right )+\textit {\_C1} \right )\right ) \left (b +x \right )]\] 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))
Maple raw output
[y(x) = -a-tan(RootOf(-2*_Z+ln(tan(_Z))+ln(b+x)+_C1))*(b+x)]