ODE
\[ (x-a) (x-b) y'(x)+k y(x)=0 \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.180766 (sec), leaf count = 34
\[\left \{\left \{y(x)\to c_1 e^{\frac {k (\log (x-b)-\log (x-a))}{a-b}}\right \}\right \}\]
Maple ✓
cpu = 0.043 (sec), leaf count = 37
\[\left [y \left (x \right ) = \textit {\_C1} \left (x -a \right )^{-\frac {k}{a -b}} \left (x -b \right )^{\frac {k}{a -b}}\right ]\] Mathematica raw input
DSolve[k*y[x] + (-a + x)*(-b + x)*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> E^((k*(-Log[-a + x] + Log[-b + x]))/(a - b))*C[1]}}
Maple raw input
dsolve((x-a)*(x-b)*diff(y(x),x)+k*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*(x-a)^(-k/(a-b))*(x-b)^(k/(a-b))]