ODE
\[ y''''''''(x)=y(x) \] ODE Classification
[[_high_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.16026 (sec), leaf count = 105
\[\left \{\left \{y(x)\to c_1 e^x+c_5 e^{-x}+c_3 \cos (x)+e^{-\frac {x}{\sqrt {2}}} \left (c_2 e^{\sqrt {2} x}+c_4\right ) \cos \left (\frac {x}{\sqrt {2}}\right )+c_7 \sin (x)+c_6 e^{-\frac {x}{\sqrt {2}}} \sin \left (\frac {x}{\sqrt {2}}\right )+c_8 e^{\frac {x}{\sqrt {2}}} \sin \left (\frac {x}{\sqrt {2}}\right )\right \}\right \}\]
Maple ✓
cpu = 0.024 (sec), leaf count = 89
\[\left [y \left (x \right ) = {\mathrm e}^{-x} \textit {\_C1} +\textit {\_C2} \,{\mathrm e}^{x}+\textit {\_C3} \sin \left (x \right )+\textit {\_C4} \cos \left (x \right )-\textit {\_C5} \,{\mathrm e}^{-\frac {\sqrt {2}\, x}{2}} \sin \left (\frac {\sqrt {2}\, x}{2}\right )-\textit {\_C6} \,{\mathrm e}^{\frac {\sqrt {2}\, x}{2}} \sin \left (\frac {\sqrt {2}\, x}{2}\right )+\textit {\_C7} \,{\mathrm e}^{-\frac {\sqrt {2}\, x}{2}} \cos \left (\frac {\sqrt {2}\, x}{2}\right )+\textit {\_C8} \,{\mathrm e}^{\frac {\sqrt {2}\, x}{2}} \cos \left (\frac {\sqrt {2}\, x}{2}\right )\right ]\] 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))
Maple raw output
[y(x) = exp(-x)*_C1+_C2*exp(x)+_C3*sin(x)+_C4*cos(x)-_C5*exp(-1/2*2^(1/2)*x)*sin(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)]