Understanding Periodic Matter Driven Neutrino Oscillations

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I have an analytical expression using two folds of approximations.

To check out how good the expression is doing, I need to verify at three levels.

1. Compare the solution to the equation I have after the first RWA approximation and the final result;
2. Compare the solution to the equation I have after the first RWA approximation and the solution to the original equation;
3. IF the solution works well in the previous two comparisons, compare the solution to the original equation and the final analytical expression.

Before doing anything, check if it is possible to find an analytical solution to the RWA approximated equation!

Analytical Expressioin