ODE
\[ y''''''(x)+a y(x)=0 \] ODE Classification
[[_high_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.159319 (sec), leaf count = 98
\[\left \{\left \{y(x)\to c_2 e^{(-1)^{5/6} \sqrt [6]{a} x}+c_3 e^{-\sqrt [6]{-1} \sqrt [6]{a} x}+c_5 e^{-(-1)^{5/6} \sqrt [6]{a} x}+c_6 e^{\sqrt [6]{-1} \sqrt [6]{a} x}+c_1 \cos \left (\sqrt [6]{a} x\right )+c_4 \sin \left (\sqrt [6]{a} x\right )\right \}\right \}\]
Maple ✓
cpu = 0.023 (sec), leaf count = 102
\[\left [y \left (x \right ) = \textit {\_C1} \,{\mathrm e}^{-\frac {\left (-1+i \sqrt {3}\right ) \left (-a \right )^{\frac {1}{6}} x}{2}}+\textit {\_C2} \,{\mathrm e}^{-\frac {\left (1+i \sqrt {3}\right ) \left (-a \right )^{\frac {1}{6}} x}{2}}+\textit {\_C3} \,{\mathrm e}^{\frac {\left (-1+i \sqrt {3}\right ) \left (-a \right )^{\frac {1}{6}} x}{2}}+\textit {\_C4} \,{\mathrm e}^{\frac {\left (1+i \sqrt {3}\right ) \left (-a \right )^{\frac {1}{6}} x}{2}}+\textit {\_C5} \,{\mathrm e}^{-\left (-a \right )^{\frac {1}{6}} x}+\textit {\_C6} \,{\mathrm e}^{\left (-a \right )^{\frac {1}{6}} x}\right ]\] Mathematica raw input
DSolve[a*y[x] + y''''''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> E^((-1)^(5/6)*a^(1/6)*x)*C[2] + C[3]/E^((-1)^(1/6)*a^(1/6)*x) + C[5]/E^((-1)^(5/6)*a^(1/6)*x) + E^((-1)^(1/6)*a^(1/6)*x)*C[6] + C[1]*Cos[a^(1/6)*x] + C[4]*Sin[a^(1/6)*x]}}
Maple raw input
dsolve(diff(diff(diff(diff(diff(diff(y(x),x),x),x),x),x),x)+a*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*exp(-1/2*(-1+I*3^(1/2))*(-a)^(1/6)*x)+_C2*exp(-1/2*(1+I*3^(1/2))*(-a)^(1/6)*x)+_C3*exp(1/2*(-1+I*3^(1/2))*(-a)^(1/6)*x)+_C4*exp(1/2*(1+I*3^(1/2))*(-a)^(1/6)*x)+_C5*exp(-(-a)^(1/6)*x)+_C6*exp((-a)^(1/6)*x)]