91Ó°ÊÓ

Determine the power series solution of the differential equation: \(\frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}+x \frac{\mathrm{d} y}{\mathrm{~d} x}+2 y=0\) using the Leibniz-Maclaurin method, given the boundary conditions that at \(x=0, y=1\) and \(\frac{\mathrm{d} y}{\mathrm{~d} x}=2\)

Determine the general power series solution of Bessel's equation.

Determine the Legendre polynomial \(P_{3}(x)\)

Determine the Legendre polynomial \(P_{2}(x)\) using Rodrigues' formula.

Determine the Legendre polynomial \(P_{3}(x)\) using Rodrigues' formula.