2.7.5.4 ✓ Sympy. Time used: 0.144 (sec). Leaf size: 32

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(-a**4*y(x) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\begin{gather*} \begin {aligned} y{\left (x \right )} = C_{1} e^{- a x} + C_{2} e^{a x} + C_{3} e^{- i a x} + C_{4} e^{i a x} \end {aligned} \end{gather*}

Python version: 3.12.3 (main, Aug 14 2025, 17:47:21) [GCC 13.3.0] 
Sympy version 1.14.0
 

classify_ode(ode,func=y(x)) 
 
('nth_linear_constant_coeff_homogeneous',)