ODE
\[ (x-a) (x-b) y'(x)=c y(x)^2 \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.447557 (sec), leaf count = 39
\[\left \{\left \{y(x)\to \frac {b-a}{c_1 (a-b)+c \log (x-a)-c \log (x-b)}\right \}\right \}\]
Maple ✓
cpu = 0.026 (sec), leaf count = 38
\[\left [y \left (x \right ) = -\frac {a -b}{c \ln \left (x -a \right )-c \ln \left (x -b \right )-\textit {\_C1} a +\textit {\_C1} b}\right ]\] Mathematica raw input
DSolve[(-a + x)*(-b + x)*y'[x] == c*y[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> (-a + b)/((a - b)*C[1] + c*Log[-a + x] - c*Log[-b + x])}}
Maple raw input
dsolve((x-a)*(x-b)*diff(y(x),x) = c*y(x)^2, y(x))
Maple raw output
[y(x) = -(a-b)/(c*ln(x-a)-c*ln(x-b)-_C1*a+_C1*b)]