Show me how to solve the diff eqn m^4-2αm^2-β=0
This is not a differential equation. It is a quadratic expression in m^2.
Let x = m^2, then the equation is
x^2 – 2αx – β = 0
Using the quadratic formula,
x = (2α ± √((-2α)^2 – 4.1. (-β)) / (2*1)
x = (2α ± √(4α^2 + 4β) / (2)
x = α ± √(α^2 + β)
x = α + √(α^2 + β), X = α - √(α^2 + β)
But x = m^2, therefore
m = ± √( α + √(α^2 + β)), m = ± √( α - √(α^2 + β))