4.29.17 \((a+b x) y''(x)+c y'(x)=0\)

ODE
\[ (a+b x) y''(x)+c y'(x)=0 \] ODE Classification

[[_2nd_order, _missing_y]]

Book solution method
TO DO

Mathematica
cpu = 0.0170434 (sec), leaf count = 32

\[\left \{\left \{y(x)\to \frac {c_1 (a+b x)^{1-\frac {c}{b}}}{b-c}+c_2\right \}\right \}\]

Maple
cpu = 0.01 (sec), leaf count = 25

\[ \left \{ y \left ( x \right ) ={\it \_C1}+{\it \_C2}\, \left ( x+{\frac {a}{b}} \right ) ^{{\frac {b-c}{b}}} \right \} \] Mathematica raw input

DSolve[c*y'[x] + (a + b*x)*y''[x] == 0,y[x],x]

Mathematica raw output

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

Maple raw input

dsolve((b*x+a)*diff(diff(y(x),x),x)+c*diff(y(x),x) = 0, y(x),'implicit')

Maple raw output

y(x) = _C1+_C2*(x+a/b)^((b-c)/b)