ODE
\[ y'''(x)-4 y''(x)+5 y'(x)-2 y(x)=0 \] ODE Classification
[[_3rd_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0091068 (sec), leaf count = 22
\[\left \{\left \{y(x)\to e^x \left (c_2 x+c_3 e^x+c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.008 (sec), leaf count = 19
\[ \left \{ y \left ( x \right ) ={{\rm e}^{2\,x}}{\it \_C1}+{{\rm e}^{x}} \left ( {\it \_C3}\,x+{\it \_C2} \right ) \right \} \] Mathematica raw input
DSolve[-2*y[x] + 5*y'[x] - 4*y''[x] + y'''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> E^x*(C[1] + x*C[2] + E^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) = 0, y(x),'implicit')
Maple raw output
y(x) = exp(2*x)*_C1+exp(x)*(_C3*x+_C2)