ODE
\[ y'''(x)-3 y''(x)+4 y'(x)-2 y(x)=e^x+\cos (x) \] ODE Classification
[[_3rd_order, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.335588 (sec), leaf count = 40
\[\left \{\left \{y(x)\to e^x (x+c_3)+\left (\frac {1}{10}+c_2 e^x\right ) \cos (x)+\left (\frac {3}{10}+c_1 e^x\right ) \sin (x)\right \}\right \}\]
Maple ✓
cpu = 0.471 (sec), leaf count = 33
\[\left [y \left (x \right ) = x \,{\mathrm e}^{x}+\frac {\cos \left (x \right )}{10}+\frac {3 \sin \left (x \right )}{10}+\textit {\_C1} \,{\mathrm e}^{x}+\textit {\_C2} \,{\mathrm e}^{x} \cos \left (x \right )+\textit {\_C3} \,{\mathrm e}^{x} \sin \left (x \right )\right ]\] Mathematica raw input
DSolve[-2*y[x] + 4*y'[x] - 3*y''[x] + y'''[x] == E^x + Cos[x],y[x],x]
Mathematica raw output
{{y[x] -> E^x*(x + C[3]) + (1/10 + E^x*C[2])*Cos[x] + (3/10 + E^x*C[1])*Sin[x]}}
Maple raw input
dsolve(diff(diff(diff(y(x),x),x),x)-3*diff(diff(y(x),x),x)+4*diff(y(x),x)-2*y(x) = exp(x)+cos(x), y(x))
Maple raw output
[y(x) = x*exp(x)+1/10*cos(x)+3/10*sin(x)+_C1*exp(x)+_C2*exp(x)*cos(x)+_C3*exp(x)*sin(x)]