# General solution of a differential equation with exponantial terms

How can I get a general solution to the following ode? dsolve command in Wolfram Mathematica and Maple don't return any result

DSolve[((5 (-10 + 3 E^(t \[Alpha])) \[Alpha]^2)/(
9 (-1 + E^(t \[Alpha]))^2) + (
E^(2 t \[Alpha]) (-1 + E^(-t \[Alpha]))^(
1/3) \[CapitalOmega]^2)/((-1 + E^(t \[Alpha]))^2
\!$$\*SubsuperscriptBox[\(a$$, $$0$$, $$2$$]\))) T[t] - (
5 E^(-t \[Alpha]) \[Alpha] T'[t])/(
2 (-1 + E^(-t \[Alpha]))) + T''[t] == 0, {T[t],
T[t]}, {t}]


• Change (T^\[Prime]\[Prime])[t] to T''[t]- But ode can't be solved analytically. I also tried transformation T[t]==F[u=Exp[\[Alpha]t] but it remains unsolvable. Jun 17 at 11:16
• The sub t -> -(Log[1 + v^3]/\[Alpha]) turns the DE into a holonomic one that yields a DifferentialRoot solution, probably with branch-cut/singularity issues, which I could not resolve because I couldn't get the solution to evaluate. Jun 17 at 14:34