ODE
\[ (a+x) y'(x)=b+c y(x) \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.0104212 (sec), leaf count = 20
\[\left \{\left \{y(x)\to c_1 (a+x)^c-\frac {b}{c}\right \}\right \}\]
Maple ✓
cpu = 0.01 (sec), leaf count = 18
\[ \left \{ y \left ( x \right ) =-{\frac {b}{c}}+ \left ( a+x \right ) ^{c}{\it \_C1} \right \} \] Mathematica raw input
DSolve[(a + x)*y'[x] == b + c*y[x],y[x],x]
Mathematica raw output
{{y[x] -> -(b/c) + (a + x)^c*C[1]}}
Maple raw input
dsolve((a+x)*diff(y(x),x) = b+c*y(x), y(x),'implicit')
Maple raw output
y(x) = -b/c+(a+x)^c*_C1