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Ordinary Differential Equations-Mathematical Physics-Assignment, Exercises of Mathematical Physics

This assignment is for Mathematical Physics course. It was assigned by Dr. Akshat Nair at Central University of Odisha. It includes: Ordinary, Differential, Equation, Adjoint, Wighting, Function, Helmholz, Legendre, Bessel, Hermite

Typology: Exercises

2011/2012

Uploaded on 07/19/2012

madan
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Mathematical Methods Assignment Number 1. PAM -507 Due date January 25, 2011 Question 1. Put the following Ordinary Differential Equations (ODE) in to self adjoint form. Also specify the differential operator and the weighting function. (a) y’ +Ay=0 (Helmholz Equation) (b) (1-x’) y” -2xy! + Ay =0 (Legendre Equation) (c) x*y+xy' + (Ax?-n”)y=0 (Bessel Equation) (d) y" -2xy' + hy =0 (Hermite Equation) Note that A is a parameter. Question 2. Solve the following equations and state whether the solutions are unique or not. Specify the conditions for which the solutions are linearly dependent. (a) y" -6y' + 9y =0 with the BC y(0)=1 and y(1)=3 (b) y’ + (cot x)y =0 find general solutions Question 3 Solve the following equations and determine the Wronskian. (a) x’ y" -5xy/ +25y =0 (b)y" =0 Question 4 Using the Wronskian determinant, show that the set of functions {i (n=12,..N)} is linearly independent. docsity.com