ODE
\[ (y(x)+x)^2 y'(x)=(y(x)+x+2)^2 \] ODE Classification
[[_homogeneous, `class C`], _rational, _dAlembert]
Book solution method
Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)
Mathematica ✓
cpu = 0.465418 (sec), leaf count = 27
\[\text {Solve}\left [\log \left ((y(x)+x+2)^2-2 (y(x)+x+2)+2\right )+x+c_1=y(x),y(x)\right ]\]
Maple ✓
cpu = 0.179 (sec), leaf count = 28
\[[-\textit {\_C1} +x -y \left (x \right )+\ln \left (\left (x +y \left (x \right )\right )^{2}+2 x +2 y \left (x \right )+2\right ) = 0]\] Mathematica raw input
DSolve[(x + y[x])^2*y'[x] == (2 + x + y[x])^2,y[x],x]
Mathematica raw output
Solve[x + C[1] + Log[2 - 2*(2 + x + y[x]) + (2 + x + y[x])^2] == y[x], y[x]]
Maple raw input
dsolve((x+y(x))^2*diff(y(x),x) = (2+x+y(x))^2, y(x))
Maple raw output
[-_C1+x-y(x)+ln((x+y(x))^2+2*x+2*y(x)+2) = 0]