4.45.38 \(2 y'''(x)+y''''(x)-2 y'(x)-y(x)=0\)

ODE
\[ 2 y'''(x)+y''''(x)-2 y'(x)-y(x)=0 \] ODE Classification

[[_high_order, _missing_x]]

Book solution method
TO DO

Mathematica
cpu = 0.00860763 (sec), leaf count = 32

\[\left \{\left \{y(x)\to e^{-x} \left (c_3 x^2+c_2 x+c_4 e^{2 x}+c_1\right )\right \}\right \}\]

Maple
cpu = 0.009 (sec), leaf count = 24

\[ \left \{ y \left ( x \right ) = \left ( {\it \_C4}\,{x}^{2}+{\it \_C3}\,x+{\it \_C2} \right ) {{\rm e}^{-x}}+{\it \_C1}\,{{\rm e}^{x}} \right \} \] Mathematica raw input

DSolve[-y[x] - 2*y'[x] + 2*y'''[x] + y''''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> (C[1] + x*C[2] + x^2*C[3] + E^(2*x)*C[4])/E^x}}

Maple raw input

dsolve(diff(diff(diff(diff(y(x),x),x),x),x)+2*diff(diff(diff(y(x),x),x),x)-2*diff(y(x),x)-y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = (_C4*x^2+_C3*x+_C2)*exp(-x)+_C1*exp(x)