Question: Use the given change of variables to transform the differential equation into one whose general solution can be written in terms of Bessel functions. Use this to write the general solution of the original differential equation.

1. Show that for any positive integer \(\nu\),
   \[x^{2} J_{\nu}^{\prime \prime}(x)=\left(\nu^{2}-\nu-x^{2}\right) J_{\nu}(x)+x J_{\nu+1}(x) .\]
   Hint: First prove \(x J_{\nu}^{\prime}(x)=\nu J_{\nu}(x)-x J_{\nu+1}(x)\).
2. Show that

Price: $2.99

Solution: The downloadable solution consists of 2 pages
Deliverable: Word Document