ODE
\[ y'''(x)-y''(x)-2 y'(x)=0 \] ODE Classification
[[_3rd_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0170805 (sec), leaf count = 28
\[\left \{\left \{y(x)\to c_1 \left (-e^{-x}\right )+\frac {1}{2} c_2 e^{2 x}+c_3\right \}\right \}\]
Maple ✓
cpu = 0.01 (sec), leaf count = 18
\[ \left \{ y \left ( x \right ) ={\it \_C1}+{{\rm e}^{2\,x}}{\it \_C2}+{\it \_C3}\,{{\rm e}^{-x}} \right \} \] Mathematica raw input
DSolve[-2*y'[x] - y''[x] + y'''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -(C[1]/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) = 0, y(x),'implicit')
Maple raw output
y(x) = _C1+exp(2*x)*_C2+_C3*exp(-x)