ODE
\[ y''''''''(x)=y(x) \] ODE Classification
[[_high_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0100168 (sec), leaf count = 105
\[\left \{\left \{y(x)\to c_1 e^x+c_5 e^{-x}+c_7 \sin (x)+c_6 e^{-\frac {x}{\sqrt {2}}} \sin \left (\frac {x}{\sqrt {2}}\right )+c_8 e^{\frac {x}{\sqrt {2}}} \sin \left (\frac {x}{\sqrt {2}}\right )+c_3 \cos (x)+e^{-\frac {x}{\sqrt {2}}} \left (c_2 e^{\sqrt {2} x}+c_4\right ) \cos \left (\frac {x}{\sqrt {2}}\right )\right \}\right \}\]
Maple ✓
cpu = 0.034 (sec), leaf count = 84
\[ \left \{ y \left ( x \right ) = \left ( -{\it \_C5}\,{{\rm e}^{-{\frac {\sqrt {2}x}{2}}}}-{\it \_C6}\,{{\rm e}^{{\frac {\sqrt {2}x}{2}}}} \right ) \sin \left ( {\frac {\sqrt {2}x}{2}} \right ) +{\it \_C7}\,{{\rm e}^{-{\frac {\sqrt {2}x}{2}}}}\cos \left ( {\frac {\sqrt {2}x}{2}} \right ) +{\it \_C8}\,{{\rm e}^{{\frac {\sqrt {2}x}{2}}}}\cos \left ( {\frac {\sqrt {2}x}{2}} \right ) +{\it \_C4}\,\cos \left ( x \right ) +{\it \_C2}\,{{\rm e}^{x}}+{\it \_C3}\,\sin \left ( x \right ) +{\it \_C1}\,{{\rm e}^{-x}} \right \} \] Mathematica raw input
DSolve[y''''''''[x] == y[x],y[x],x]
Mathematica raw output
{{y[x] -> E^x*C[1] + C[5]/E^x + C[3]*Cos[x] + ((E^(Sqrt[2]*x)*C[2] + C[4])*Cos[x/Sqrt[2]])/E^(x/Sqrt[2]) + C[7]*Sin[x] + (C[6]*Sin[x/Sqrt[2]])/E^(x/Sqrt[2]) + E^(x/Sqrt[2])*C[8]*Sin[x/Sqrt[2]]}}
Maple raw input
dsolve(diff(diff(diff(diff(diff(diff(diff(diff(y(x),x),x),x),x),x),x),x),x) = y(x), y(x),'implicit')
Maple raw output
y(x) = (-_C5*exp(-1/2*2^(1/2)*x)-_C6*exp(1/2*2^(1/2)*x))*sin(1/2*2^(1/2)*x)+_C7*exp(-1/2*2^(1/2)*x)*cos(1/2*2^(1/2)*x)+_C8*exp(1/2*2^(1/2)*x)*cos(1/2*2^(1/2)*x)+_C4*cos(x)+_C2*exp(x)+_C3*sin(x)+_C1*exp(-x)