ODE
\[ y'''(x)-a^2 y'(x)+2 a^2 y(x)-2 y''(x)=0 \] ODE Classification
[[_3rd_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0087241 (sec), leaf count = 31
\[\left \{\left \{y(x)\to c_1 e^{-a x}+c_3 e^{a x}+c_2 e^{2 x}\right \}\right \}\]
Maple ✓
cpu = 0.01 (sec), leaf count = 24
\[ \left \{ y \left ( x \right ) ={{\rm e}^{2\,x}}{\it \_C1}+{\it \_C2}\,{{\rm e}^{-ax}}+{\it \_C3}\,{{\rm e}^{ax}} \right \} \] Mathematica raw input
DSolve[2*a^2*y[x] - a^2*y'[x] - 2*y''[x] + y'''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[1]/E^(a*x) + E^(2*x)*C[2] + E^(a*x)*C[3]}}
Maple raw input
dsolve(diff(diff(diff(y(x),x),x),x)-2*diff(diff(y(x),x),x)-a^2*diff(y(x),x)+2*a^2*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = exp(2*x)*_C1+_C2*exp(-a*x)+_C3*exp(a*x)