ODE
\[ y'''(x)-2 y''(x)+y'(x)=e^x \] ODE Classification
[[_3rd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0232767 (sec), leaf count = 33
\[\left \{\left \{y(x)\to e^x \left (\left (c_2-1\right ) x+c_1-c_2+\frac {x^2}{2}+1\right )+c_3\right \}\right \}\]
Maple ✓
cpu = 0.02 (sec), leaf count = 28
\[ \left \{ y \left ( x \right ) ={\frac { \left ( {x}^{2}+ \left ( 2\,{\it \_C1}-2 \right ) x-2\,{\it \_C1}+2\,{\it \_C2}+2 \right ) {{\rm e}^{x}}}{2}}+{\it \_C3} \right \} \] 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),'implicit')
Maple raw output
y(x) = 1/2*(x^2+(2*_C1-2)*x-2*_C1+2*_C2+2)*exp(x)+_C3