ODE
\[ (x-a) (x-b) y'(x)+k y(x)=0 \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.0161387 (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 = 0.02 (sec), leaf count = 37
\[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( x-b \right ) ^{{\frac {k}{a-b}}} \left ( x-a \right ) ^{-{\frac {k}{a-b}}} \right \} \] 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),'implicit')
Maple raw output
y(x) = _C1*(x-b)^(k/(a-b))*(x-a)^(-k/(a-b))