4.43.39 \(y'''(x)-4 y''(x)+6 y'(x)-4 y(x)=0\)

ODE
\[ y'''(x)-4 y''(x)+6 y'(x)-4 y(x)=0 \] ODE Classification

[[_3rd_order, _missing_x]]

Book solution method
TO DO

Mathematica
cpu = 0.0126561 (sec), leaf count = 26

\[\left \{\left \{y(x)\to e^x \left (c_3 e^x+c_1 \sin (x)+c_2 \cos (x)\right )\right \}\right \}\]

Maple
cpu = 0.007 (sec), leaf count = 23

\[ \left \{ y \left ( x \right ) ={{\rm e}^{2\,x}}{\it \_C1}+{\it \_C2}\,{{\rm e}^{x}}\sin \left ( x \right ) +{\it \_C3}\,{{\rm e}^{x}}\cos \left ( x \right ) \right \} \] Mathematica raw input

DSolve[-4*y[x] + 6*y'[x] - 4*y''[x] + y'''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> E^x*(E^x*C[3] + C[2]*Cos[x] + C[1]*Sin[x])}}

Maple raw input

dsolve(diff(diff(diff(y(x),x),x),x)-4*diff(diff(y(x),x),x)+6*diff(y(x),x)-4*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = exp(2*x)*_C1+_C2*exp(x)*sin(x)+_C3*exp(x)*cos(x)