4.13.23 \(y'(x) (a+b+y(x)+x)^2=2 (a+y(x))^2\)

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 = 0.0873864 (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 = 0.028 (sec), leaf count = 47

\[ \left \{ 2\,\arctan \left ({\frac {-a-y \relax (x ) }{b+x}} \right ) -\ln \left ({\frac {-a-y \relax (x ) }{b+x}} \right ) -\ln \left (b+x \right ) -{\it \_C1}=0 \right \} \] 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),'implicit')

Maple raw output

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