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 = 0.173724 (sec), leaf count = 23
\[\left \{\left \{y(x)\to e^x (-\log (x-1)+c_2 x-1+c_1)\right \}\right \}\]
Maple ✓
cpu = 0.056 (sec), leaf count = 24
\[[y \left (x \right ) = \textit {\_C2} \,{\mathrm e}^{x}+{\mathrm e}^{x} \textit {\_C1} x -\left (\ln \left (x -1\right )+1\right ) {\mathrm e}^{x}]\] 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))
Maple raw output
[y(x) = _C2*exp(x)+exp(x)*_C1*x-(ln(x-1)+1)*exp(x)]