4.13.17 \((y(x)+x)^2 y'(x)=a^2\)

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 = 0.038709 (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 = 0.026 (sec), leaf count = 22

\[ \left \{ a\arctan \left ({\frac {x+y \relax (x ) }{a}} \right ) -y \relax (x ) -{\it \_C1}=0 \right \} \] 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),'implicit')

Maple raw output

a*arctan((x+y(x))/a)-y(x)-_C1 = 0