ODE
\[ y'''(x)-2 y'(x)+4 y(x)=e^x \cos (x) \] ODE Classification
[[_3rd_order, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0513872 (sec), leaf count = 57
\[\left \{\left \{y(x)\to \frac {1}{100} e^{-2 x} \left (e^{3 x} \left (100 c_1+15 x+1\right ) \sin (x)-e^{3 x} \left (5 x-2 \left (50 c_2+9\right )\right ) \cos (x)+100 c_3\right )\right \}\right \}\]
Maple ✓
cpu = 0.087 (sec), leaf count = 35
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{-2\,x}}-{\frac {{{\rm e}^{x}}}{20} \left ( \left ( x-20\,{\it \_C2}-{\frac {18}{5}} \right ) \cos \left ( x \right ) -3\,\sin \left ( x \right ) \left ( x+{\frac {20\,{\it \_C3}}{3}}+1/15 \right ) \right ) } \right \} \] Mathematica raw input
DSolve[4*y[x] - 2*y'[x] + y'''[x] == E^x*Cos[x],y[x],x]
Mathematica raw output
{{y[x] -> (100*C[3] - E^(3*x)*(5*x - 2*(9 + 50*C[2]))*Cos[x] + E^(3*x)*(1 + 15*x + 100*C[1])*Sin[x])/(100*E^(2*x))}}
Maple raw input
dsolve(diff(diff(diff(y(x),x),x),x)-2*diff(y(x),x)+4*y(x) = exp(x)*cos(x), y(x),'implicit')
Maple raw output
y(x) = _C1*exp(-2*x)-1/20*exp(x)*((x-20*_C2-18/5)*cos(x)-3*sin(x)*(x+20/3*_C3+1/15))