9.The Laguerre13 differential equation is xy′′+(1−x)y′+λy=0.xy″+1−xy′+λy=0. a.Show that x = 0 is a regular singular point. b.Determine the indicial equation, its roots, and the recurrence relation. c.Find one solution (for x > 0). Show that if λ = m, a positive integer, this solution reduces to a polynomial. When properly normalized, this polynomial is known as the Laguerre polynomial, Lm(x).

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.