ODE
\[ y'''(x)-2 y''(x)+y'(x)=e^x \] ODE Classification
[[_3rd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.180568 (sec), leaf count = 33
\[\left \{\left \{y(x)\to e^x \left (\frac {x^2}{2}+(-1+c_2) x+1+c_1-c_2\right )+c_3\right \}\right \}\]
Maple ✓
cpu = 0.161 (sec), leaf count = 28
\[\left [y \left (x \right ) = \frac {\left (2 \textit {\_C1} x +x^{2}-2 \textit {\_C1} +2 \textit {\_C2} -2 x +2\right ) {\mathrm e}^{x}}{2}+\textit {\_C3}\right ]\] Mathematica raw input
DSolve[y'[x] - 2*y''[x] + y'''[x] == E^x,y[x],x]
Mathematica raw output
{{y[x] -> E^x*(1 + x^2/2 + C[1] + x*(-1 + C[2]) - C[2]) + C[3]}}
Maple raw input
dsolve(diff(diff(diff(y(x),x),x),x)-2*diff(diff(y(x),x),x)+diff(y(x),x) = exp(x), y(x))
Maple raw output
[y(x) = 1/2*(2*_C1*x+x^2-2*_C1+2*_C2-2*x+2)*exp(x)+_C3]