I am trying to solve a linear second order ODE using
DSolve which involves an arbitrary integer
DSolve gives me a solution when I set
m to a particular integer (I have tried several, including negative/positive, even/odd, and
0). When I try to use the assumption
m ∈ Integers and ask
DSolve to solve this ODE for an arbitrary integer
m, it does not work.
Here is the input:
$Assumptions = m ∈ Integers testk = 0 == -16 c m^2 Cos[x] k[x] - c (-7 Sin[x] + Sin[3x]) k'[x] + Cos[x] Sin[x]^2 (m^2 (3 + 4 m Cos[x] + Cos[2 x]) Tan[x/2]^(2 m) + 4 c k''[x]) DSolve[ testk, k[x], x]
DSolve[ 0 == -16 c m^2 Cos[x] k[x] - c (-7 Sin[x] + Sin[3 x]) k'[x] + Cos[x] Sin[x]^2 (m^2 (3 + 4 m Cos[x] + Cos[2 x]) Tan[x/2]^(2 m) + 4 c k''[x], k[x], x]
I have realized that the problem is that
DSolve does not apply any of the global assumptions. Does anyone know how I can make
DSolve apply the assumption that
m ∈ Integers? I have tried using
Assuming[,] to set the assumptions locally but that did not work either.