Question: Identifying the Corresponding Solution Class for Derived ODE Solutions

I am working on obtaining the complete set of solutions for a given ordinary differential equation (ODE). While testing various cases from the auxiliary ODE method, I derived a solution of the form U(ξ). However, I am currently unable to determine which specific case or class from the established solution set this result corresponds to.

I would appreciate any guidance or method to correctly classify each obtained solution U(ξ) according to its respective case within the set of auxiliary ODE cases.

ode.mw

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