ODE
\[ y''''(x)+a y(x)=0 \] ODE Classification
[[_high_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.00750143 (sec), leaf count = 76
\[\left \{\left \{y(x)\to c_1 e^{(-1)^{3/4} \sqrt [4]{a} x}+c_2 e^{-\sqrt [4]{-1} \sqrt [4]{a} x}+c_3 e^{-(-1)^{3/4} \sqrt [4]{a} x}+c_4 e^{\sqrt [4]{-1} \sqrt [4]{a} x}\right \}\right \}\]
Maple ✓
cpu = 0.012 (sec), leaf count = 50
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{-i\sqrt [4]{-a}x}}+{\it \_C2}\,{{\rm e}^{i\sqrt [4]{-a}x}}+{\it \_C3}\,{{\rm e}^{-\sqrt [4]{-a}x}}+{\it \_C4}\,{{\rm e}^{\sqrt [4]{-a}x}} \right \} \] Mathematica raw input
DSolve[a*y[x] + y''''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> E^((-1)^(3/4)*a^(1/4)*x)*C[1] + C[2]/E^((-1)^(1/4)*a^(1/4)*x) + C[3]/E^((-1)^(3/4)*a^(1/4)*x) + E^((-1)^(1/4)*a^(1/4)*x)*C[4]}}
Maple raw input
dsolve(diff(diff(diff(diff(y(x),x),x),x),x)+a*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = _C1*exp(-I*(-a)^(1/4)*x)+_C2*exp(I*(-a)^(1/4)*x)+_C3*exp(-(-a)^(1/4)*x)+_C4*exp((-a)^(1/4)*x)