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

ODE
\[ (a+x) y'(x)=b x+c y(x) \] ODE Classification

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.0163371 (sec), leaf count = 32

\[\left \{\left \{y(x)\to \frac {a b+b c x}{c-c^2}+c_1 (a+x)^c\right \}\right \}\]

Maple
cpu = 0.01 (sec), leaf count = 28

\[ \left \{ y \relax (x ) = \left (a+x \right ) ^{c}{\it \_C1}-{\frac {b \left (cx+a \right ) }{c \left (c-1 \right ) }} \right \} \] Mathematica raw input

DSolve[(a + x)*y'[x] == b*x + c*y[x],y[x],x]

Mathematica raw output

{{y[x] -> (a*b + b*c*x)/(c - c^2) + (a + x)^c*C[1]}}

Maple raw input

dsolve((a+x)*diff(y(x),x) = b*x+c*y(x), y(x),'implicit')

Maple raw output

y(x) = (a+x)^c*_C1-b*(c*x+a)/c/(c-1)