ODE
\[ (x-a) (x-b) y'(x)=y(x) (-a-b+2 x)+(x-a) (x-b) \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.0257433 (sec), leaf count = 42
\[\left \{\left \{y(x)\to (x-a) (x-b) \left (\frac {\log (x-a)-\log (x-b)}{a-b}+c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.018 (sec), leaf count = 44
\[ \left \{ y \left ( x \right ) ={\frac { \left ( b-x \right ) \left ( \ln \left ( x-a \right ) -\ln \left ( x-b \right ) +{\it \_C1}\, \left ( a-b \right ) \right ) \left ( a-x \right ) }{a-b}} \right \} \] Mathematica raw input
DSolve[(-a + x)*(-b + x)*y'[x] == (-a + x)*(-b + x) + (-a - b + 2*x)*y[x],y[x],x]
Mathematica raw output
{{y[x] -> (-a + x)*(-b + x)*(C[1] + (Log[-a + x] - Log[-b + x])/(a - b))}}
Maple raw input
dsolve((x-a)*(x-b)*diff(y(x),x) = (x-a)*(x-b)+(2*x-a-b)*y(x), y(x),'implicit')
Maple raw output
y(x) = (b-x)*(ln(x-a)-ln(x-b)+_C1*(a-b))*(a-x)/(a-b)