ODE
\[ y''''(x)-2 y''(x)-8 y(x)=0 \] ODE Classification
[[_high_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.00941015 (sec), leaf count = 44
\[\left \{\left \{y(x)\to c_3 e^{-2 x}+c_4 e^{2 x}+c_2 \sin \left (\sqrt {2} x\right )+c_1 \cos \left (\sqrt {2} x\right )\right \}\right \}\]
Maple ✓
cpu = 0.009 (sec), leaf count = 33
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{2\,x}}+{\it \_C2}\,{{\rm e}^{-2\,x}}+{\it \_C3}\,\sin \left ( \sqrt {2}x \right ) +{\it \_C4}\,\cos \left ( \sqrt {2}x \right ) \right \} \] 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),'implicit')
Maple raw output
y(x) = _C1*exp(2*x)+_C2*exp(-2*x)+_C3*sin(2^(1/2)*x)+_C4*cos(2^(1/2)*x)