4.7.27 \((x-a) (x-b) y'(x)=c y(x)^2\)

ODE
\[ (x-a) (x-b) y'(x)=c y(x)^2 \] ODE Classification

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 0.0184464 (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 = 0.015 (sec), leaf count = 42

\[ \left \{ \left (y \relax (x ) \right ) ^{-1}-{\frac {c\ln \left (x-b \right ) }{a-b}}+{\frac {c\ln \left (x-a \right ) }{a-b}}-{\it \_C1}=0 \right \} \] 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),'implicit')

Maple raw output

1/y(x)-c/(a-b)*ln(x-b)+c/(a-b)*ln(x-a)-_C1 = 0