How can I get a symbolic solution from the following differential equation? I don't know in that case using a change of variable is a good idea. I have tried in maple as well but the form of the solution was not in my desire.
wave = (3 Derivative[1][a][t]/a[t] Derivative[1][T][t]) +
T[t] (\[CapitalOmega]^2/
a[t]^2 - (6 Derivative[1][a][t]^2/
a[t]^2) - (2 (a^\[Prime]\[Prime])[t]/a[t])) + (
T^\[Prime]\[Prime])[t] == 0
a[t_] := t^\[Alpha];
DSolve[(-((2 (-1 + \[Alpha]) \[Alpha])/t^2) - (6 \[Alpha]^2)/t^2 +
t^(-2 \[Alpha]) \[CapitalOmega]^2) T[t] + (
3 \[Alpha] Derivative[1][T][t])/t + (T^\[Prime]\[Prime])[t] ==
0, {T[t], T[t]}, {t}]
Thank you!
wave
for? where is it used? $\endgroup$It's gravitational waves
OK. But why do you have it is my question. Where is it used in theDSolve
command? If it is not relevant variable and not used, why show it in the question? It can make things confusing to the reader. $\endgroup$