ODE
\[ y''(x)-2 y'(x)+y(x)=e^x \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.00676547 (sec), leaf count = 25
\[\left \{\left \{y(x)\to \frac {1}{2} e^x \left (2 c_2 x+2 c_1+x^2\right )\right \}\right \}\]
Maple ✓
cpu = 0.012 (sec), leaf count = 19
\[ \left \{ y \left ( x \right ) ={\frac {{{\rm e}^{x}} \left ( 2\,{\it \_C1}\,x+{x}^{2}+2\,{\it \_C2} \right ) }{2}} \right \} \] 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),'implicit')
Maple raw output
y(x) = 1/2*exp(x)*(2*_C1*x+x^2+2*_C2)