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.

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