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 = 0.431213 (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 = 0.359 (sec), leaf count = 131
\[\left [y \left (x \right ) = \frac {\left (x -b \right )^{-k} \left (x -a \right )^{k} a \,{\mathrm e}^{\textit {\_C1} k a -\textit {\_C1} k b}-\left (x -b \right )^{-k} \left (x -a \right )^{k} b \,{\mathrm e}^{\textit {\_C1} k a -\textit {\_C1} k b}+b \left (\frac {b -x}{a -x}\right )^{-k} {\mathrm e}^{\textit {\_C1} k a -\textit {\_C1} k b}-b}{-1+\left (\frac {b -x}{a -x}\right )^{-k} {\mathrm e}^{\textit {\_C1} k a -\textit {\_C1} k b}}\right ]\] 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))
Maple raw output
[y(x) = ((x-b)^(-k)*(x-a)^k*a*exp(_C1*a*k-_C1*b*k)-(x-b)^(-k)*(x-a)^k*b*exp(_C1*a*k-_C1*b*k)+b*((b-x)/(a-x))^(-k)*exp(_C1*a*k-_C1*b*k)-b)/(-1+((b-x)/(a-x))^(-k)*exp(_C1*a*k-_C1*b*k))]