ODE
\[ y''''''(x)+a y(x)=0 \] ODE Classification
[[_high_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0083526 (sec), leaf count = 98
\[\left \{\left \{y(x)\to c_2 e^{(-1)^{5/6} \sqrt [6]{a} x}+c_3 e^{-\sqrt [6]{-1} \sqrt [6]{a} x}+c_5 e^{-(-1)^{5/6} \sqrt [6]{a} x}+c_6 e^{\sqrt [6]{-1} \sqrt [6]{a} x}+c_4 \sin \left (\sqrt [6]{a} x\right )+c_1 \cos \left (\sqrt [6]{a} x\right )\right \}\right \}\]
Maple ✓
cpu = 0.013 (sec), leaf count = 102
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{-{\frac { \left ( i\sqrt {3}-1 \right ) x}{2}\sqrt [6]{-a}}}}+{\it \_C2}\,{{\rm e}^{-{\frac { \left ( i\sqrt {3}+1 \right ) x}{2}\sqrt [6]{-a}}}}+{\it \_C3}\,{{\rm e}^{{\frac { \left ( i\sqrt {3}-1 \right ) x}{2}\sqrt [6]{-a}}}}+{\it \_C4}\,{{\rm e}^{{\frac { \left ( i\sqrt {3}+1 \right ) x}{2}\sqrt [6]{-a}}}}+{\it \_C5}\,{{\rm e}^{-\sqrt [6]{-a}x}}+{\it \_C6}\,{{\rm e}^{\sqrt [6]{-a}x}} \right \} \] 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),'implicit')
Maple raw output
y(x) = _C1*exp(-1/2*(I*3^(1/2)-1)*(-a)^(1/6)*x)+_C2*exp(-1/2*(I*3^(1/2)+1)*(-a)^(1/6)*x)+_C3*exp(1/2*(I*3^(1/2)-1)*(-a)^(1/6)*x)+_C4*exp(1/2*(I*3^(1/2)+1)*(-a)^(1/6)*x)+_C5*exp(-(-a)^(1/6)*x)+_C6*exp((-a)^(1/6)*x)