I cannot derivate the formula of . Please read the question at the bottom and look at the way how I derivate the coeficients. You can see the formula don't match.
The original question is:
Find the solution of the equation for damping vibration string stretched from x=0 to x=L where
With boundary and initial condition given:
Using constant coeficients ODE,
Three cases of
The text book gave this equation:
I tried and I cannot arrive to this formula no matter what. Please look at (10) above.
It look very similar to the formula for .
But the book seldom make mistake!!! What did I do wrong?