ODE
\[ y''(x)-2 y'(x)+y(x)=e^x \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.159368 (sec), leaf count = 25
\[\left \{\left \{y(x)\to \frac {1}{2} e^x \left (x^2+2 c_2 x+2 c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.015 (sec), leaf count = 21
\[\left [y \left (x \right ) = \textit {\_C2} \,{\mathrm e}^{x}+{\mathrm e}^{x} \textit {\_C1} x +\frac {x^{2} {\mathrm e}^{x}}{2}\right ]\] Mathematica raw input
DSolve[y[x] - 2*y'[x] + y''[x] == E^x,y[x],x]
Mathematica raw output
{{y[x] -> (E^x*(x^2 + 2*C[1] + 2*x*C[2]))/2}}
Maple raw input
dsolve(diff(diff(y(x),x),x)-2*diff(y(x),x)+y(x) = exp(x), y(x))
Maple raw output
[y(x) = _C2*exp(x)+exp(x)*_C1*x+1/2*x^2*exp(x)]