ODE
\[ (a+x)^2 y'(x)=2 (a+x) (b+y(x)) \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.00965325 (sec), leaf count = 17
\[\left \{\left \{y(x)\to c_1 (a+x)^2-b\right \}\right \}\]
Maple ✓
cpu = 0.007 (sec), leaf count = 15
\[ \left \{ y \left ( x \right ) =-b+ \left ( a+x \right ) ^{2}{\it \_C1} \right \} \] Mathematica raw input
DSolve[(a + x)^2*y'[x] == 2*(a + x)*(b + y[x]),y[x],x]
Mathematica raw output
{{y[x] -> -b + (a + x)^2*C[1]}}
Maple raw input
dsolve((a+x)^2*diff(y(x),x) = 2*(a+x)*(b+y(x)), y(x),'implicit')
Maple raw output
y(x) = -b+(a+x)^2*_C1