ODE
\[ (a+b x) y''(x)+c y'(x)=0 \] ODE Classification
[[_2nd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.187049 (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 = 0.013 (sec), leaf count = 25
\[\left [y \left (x \right ) = \textit {\_C1} +\textit {\_C2} \left (x +\frac {a}{b}\right )^{\frac {b -c}{b}}\right ]\] 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))
Maple raw output
[y(x) = _C1+_C2*(x+a/b)^((b-c)/b)]