ODE
\[ k (y(x)-a) (y(x)-b)+(x-a) (x-b) y'(x)=0 \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.0689227 (sec), leaf count = 70
\[\left \{\left \{y(x)\to \frac {a e^{b c_1} (x-a)^k-b e^{a c_1} (x-b)^k}{e^{b c_1} (x-a)^k-e^{a c_1} (x-b)^k}\right \}\right \}\]
Maple ✓
cpu = 0.011 (sec), leaf count = 56
\[ \left \{ {\frac {\ln \left ( y \left ( x \right ) -a \right ) -\ln \left ( y \left ( x \right ) -b \right ) +\ln \left ( x-a \right ) k-\ln \left ( x-b \right ) k+{\it \_C1}\,k \left ( a-b \right ) }{k \left ( a-b \right ) }}=0 \right \} \] Mathematica raw input
DSolve[k*(-a + y[x])*(-b + y[x]) + (-a + x)*(-b + x)*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (a*E^(b*C[1])*(-a + x)^k - b*E^(a*C[1])*(-b + x)^k)/(E^(b*C[1])*(-a + x)^k - E^(a*C[1])*(-b + x)^k)}}
Maple raw input
dsolve((x-a)*(x-b)*diff(y(x),x)+k*(y(x)-a)*(y(x)-b) = 0, y(x),'implicit')
Maple raw output
(ln(y(x)-a)-ln(y(x)-b)+ln(x-a)*k-ln(x-b)*k+_C1*k*(a-b))/k/(a-b) = 0