4.5.35 \((a+x) y'(x)=b+c y(x)\)

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

\[ \left \{ y \relax (x ) =-{\frac {b}{c}}+ \left (a+x \right ) ^{c}{\it \_C1} \right \} \] 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