ODE
\[ y'''(x)-4 y''(x)+5 y'(x)-2 y(x)=x \] ODE Classification
[[_3rd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.159824 (sec), leaf count = 35
\[\left \{\left \{y(x)\to c_1 e^x+x \left (-\frac {1}{2}+c_2 e^x\right )+c_3 e^{2 x}-\frac {5}{4}\right \}\right \}\]
Maple ✓
cpu = 0.018 (sec), leaf count = 24
\[\left [y \left (x \right ) = -\frac {x}{2}-\frac {5}{4}+\textit {\_C1} \,{\mathrm e}^{x}+\textit {\_C2} \,{\mathrm e}^{2 x}+\textit {\_C3} \,{\mathrm e}^{x} x\right ]\] Mathematica raw input
DSolve[-2*y[x] + 5*y'[x] - 4*y''[x] + y'''[x] == x,y[x],x]
Mathematica raw output
{{y[x] -> -5/4 + E^x*C[1] + x*(-1/2 + E^x*C[2]) + E^(2*x)*C[3]}}
Maple raw input
dsolve(diff(diff(diff(y(x),x),x),x)-4*diff(diff(y(x),x),x)+5*diff(y(x),x)-2*y(x) = x, y(x))
Maple raw output
[y(x) = -1/2*x-5/4+_C1*exp(x)+_C2*exp(2*x)+_C3*exp(x)*x]