ODE
\[ y'''(x)-6 y''(x)+9 y'(x)=0 \] ODE Classification
[[_3rd_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0220954 (sec), leaf count = 30
\[\left \{\left \{y(x)\to \frac {1}{9} e^{3 x} \left (c_2 (3 x-1)+3 c_1\right )+c_3\right \}\right \}\]
Maple ✓
cpu = 0.007 (sec), leaf count = 16
\[ \left \{ y \left ( x \right ) ={{\rm e}^{3\,x}} \left ( {\it \_C3}\,x+{\it \_C2} \right ) +{\it \_C1} \right \} \] Mathematica raw input
DSolve[9*y'[x] - 6*y''[x] + y'''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (E^(3*x)*(3*C[1] + (-1 + 3*x)*C[2]))/9 + C[3]}}
Maple raw input
dsolve(diff(diff(diff(y(x),x),x),x)-6*diff(diff(y(x),x),x)+9*diff(y(x),x) = 0, y(x),'implicit')
Maple raw output
y(x) = exp(3*x)*(_C3*x+_C2)+_C1