ODE
\[ y''''(x)-2 y''(x)-8 y(x)=0 \] ODE Classification
[[_high_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.151936 (sec), leaf count = 44
\[\left \{\left \{y(x)\to c_3 e^{-2 x}+c_4 e^{2 x}+c_1 \cos \left (\sqrt {2} x\right )+c_2 \sin \left (\sqrt {2} x\right )\right \}\right \}\]
Maple ✓
cpu = 0.014 (sec), leaf count = 33
\[\left [y \left (x \right ) = {\mathrm e}^{-2 x} \textit {\_C1} +\textit {\_C2} \,{\mathrm e}^{2 x}+\textit {\_C3} \sin \left (\sqrt {2}\, x \right )+\textit {\_C4} \cos \left (\sqrt {2}\, x \right )\right ]\] Mathematica raw input
DSolve[-8*y[x] - 2*y''[x] + y''''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[3]/E^(2*x) + E^(2*x)*C[4] + C[1]*Cos[Sqrt[2]*x] + C[2]*Sin[Sqrt[2]*x]}}
Maple raw input
dsolve(diff(diff(diff(diff(y(x),x),x),x),x)-2*diff(diff(y(x),x),x)-8*y(x) = 0, y(x))
Maple raw output
[y(x) = exp(-2*x)*_C1+_C2*exp(2*x)+_C3*sin(2^(1/2)*x)+_C4*cos(2^(1/2)*x)]