ODE
\[ y'''(x)-y''(x)-2 y'(x)=e^{-x} \] ODE Classification
[[_3rd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0490091 (sec), leaf count = 37
\[\left \{\left \{y(x)\to \frac {1}{9} e^{-x} \left (-9 c_1+3 x+4\right )+\frac {1}{2} c_2 e^{2 x}+c_3\right \}\right \}\]
Maple ✓
cpu = 0.025 (sec), leaf count = 27
\[ \left \{ y \left ( x \right ) ={\frac { \left ( 2\,x-6\,{\it \_C2}+2 \right ) {{\rm e}^{-x}}}{6}}+{\frac {{{\rm e}^{2\,x}}{\it \_C1}}{2}}+{\it \_C3} \right \} \] 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),'implicit')
Maple raw output
y(x) = 1/6*(2*x-6*_C2+2)*exp(-x)+1/2*exp(2*x)*_C1+_C3