Solution Found!
Show that the differential equation can be transformed
Chapter 6, Problem 46E(choose chapter or problem)
Show that the differential equation
\(\sin \theta \frac{d^{2} y}{d \theta^{2}}+\cos \theta \frac{d y}{d \theta}+n(n+1)(\sin \theta) y=0\)
can be transformed into Legendre’s equation by means of the substitution \(x=\cos \theta\).
Text Transcription:
sinthetafracd^2ydtheta^2+costhetafracdydtheta+n(n+1)(sintheta)y=0
x=cos\theta
Questions & Answers
QUESTION:
Show that the differential equation
\(\sin \theta \frac{d^{2} y}{d \theta^{2}}+\cos \theta \frac{d y}{d \theta}+n(n+1)(\sin \theta) y=0\)
can be transformed into Legendre’s equation by means of the substitution \(x=\cos \theta\).
Text Transcription:
sinthetafracd^2ydtheta^2+costhetafracdydtheta+n(n+1)(sintheta)y=0
x=cos\theta
ANSWER:Step 1 of 3
In this problem we have to show that the given differential equation can be transformed into Legendre’s equation.