Using the transformation (x=cosh t), show that the differential equation (frac{d^{2} y}{d t^{2}}+) (operatorname{coth} t frac{d y}{d

Question:

Using the transformation \(x=\cosh t\), show that the differential equation \(\frac{d^{2} y}{d t^{2}}+\) \(\operatorname{coth} t \frac{d y}{d t}-20 y=0\) reduces to Legendre's differential equation and give the expression for the Legendre polynomial which is a solution to this transformed equation.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For  book-img-for-question

Advanced Mathematics For Engineering Students The Essential Toolbox

ISBN: 9780128236826

1st Edition

Authors: Brent J Lewis, Nihan Onder, E Nihan Onder, Andrew Prudil

Question Posted: