ODE
\[ y'''(x)-y''(x)-2 y'(x)=e^{-x} \] ODE Classification
[[_3rd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.221283 (sec), leaf count = 37
\[\left \{\left \{y(x)\to \frac {1}{9} e^{-x} (3 x+4-9 c_1)+\frac {1}{2} c_2 e^{2 x}+c_3\right \}\right \}\]
Maple ✓
cpu = 0.288 (sec), leaf count = 33
\[\left [y \left (x \right ) = -\textit {\_C2} \,{\mathrm e}^{-x}+\frac {{\mathrm e}^{2 x} \textit {\_C1}}{2}+\frac {x \,{\mathrm e}^{-x}}{3}+\frac {{\mathrm e}^{-x}}{3}+\textit {\_C3}\right ]\] Mathematica raw input
DSolve[-2*y'[x] - y''[x] + y'''[x] == E^(-x),y[x],x]
Mathematica raw output
{{y[x] -> (4 + 3*x - 9*C[1])/(9*E^x) + (E^(2*x)*C[2])/2 + C[3]}}
Maple raw input
dsolve(diff(diff(diff(y(x),x),x),x)-diff(diff(y(x),x),x)-2*diff(y(x),x) = exp(-x), y(x))
Maple raw output
[y(x) = -_C2*exp(-x)+1/2*exp(2*x)*_C1+1/3*x*exp(-x)+1/3*exp(-x)+_C3]