ODE
\[ (1-x)^2 y''(x)-2 (1-x)^2 y'(x)+(1-x)^2 y(x)=e^x \] ODE Classification
[[_2nd_order, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0412875 (sec), leaf count = 23
\[\left \{\left \{y(x)\to e^x \left (c_2 x+c_1-\log (x-1)-1\right )\right \}\right \}\]
Maple ✓
cpu = 0.03 (sec), leaf count = 19
\[ \left \{ y \left ( x \right ) ={{\rm e}^{x}} \left ( {\it \_C1}\,x+{\it \_C2}-\ln \left ( -1+x \right ) -1 \right ) \right \} \] Mathematica raw input
DSolve[(1 - x)^2*y[x] - 2*(1 - x)^2*y'[x] + (1 - x)^2*y''[x] == E^x,y[x],x]
Mathematica raw output
{{y[x] -> E^x*(-1 + C[1] + x*C[2] - Log[-1 + x])}}
Maple raw input
dsolve((1-x)^2*diff(diff(y(x),x),x)-2*(1-x)^2*diff(y(x),x)+(1-x)^2*y(x) = exp(x), y(x),'implicit')
Maple raw output
y(x) = exp(x)*(_C1*x+_C2-ln(-1+x)-1)