ODE
\[ (y(x)+x)^2 y'(x)=a^2 \] ODE Classification
[[_homogeneous, `class C`], _dAlembert]
Book solution method
Equation linear in the variables, \(y'(x)=f(a+b x+ c y(x))\)
Mathematica ✓
cpu = 0.374245 (sec), leaf count = 20
\[\text {Solve}\left [a \tan ^{-1}\left (\frac {y(x)+x}{a}\right )+c_1=y(x),y(x)\right ]\]
Maple ✓
cpu = 0.066 (sec), leaf count = 24
\[[y \left (x \right ) = a \RootOf \left (\tan \left (\textit {\_Z} \right ) a -a \textit {\_Z} +\textit {\_C1} -x \right )-\textit {\_C1}]\] Mathematica raw input
DSolve[(x + y[x])^2*y'[x] == a^2,y[x],x]
Mathematica raw output
Solve[a*ArcTan[(x + y[x])/a] + C[1] == y[x], y[x]]
Maple raw input
dsolve((x+y(x))^2*diff(y(x),x) = a^2, y(x))
Maple raw output
[y(x) = a*RootOf(tan(_Z)*a-a*_Z+_C1-x)-_C1]