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 = 0.165771 (sec), leaf count = 17
\[\left \{\left \{y(x)\to -b+c_1 (a+x)^2\right \}\right \}\]
Maple ✓
cpu = 0.008 (sec), leaf count = 15
\[[y \left (x \right ) = -b +\left (a +x \right )^{2} \textit {\_C1}]\] 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))
Maple raw output
[y(x) = -b+(a+x)^2*_C1]