(b) What are the singular points, if any, of each of the following ordinary differentialequations?(i)a(r – 1)y" + (3r – 1)y/ + y = 0.(ii)xy" + (x – 6)y – 3y = 0(iii)y" + (In r)y = 0

A function f is said to be analytic at x0 if - Taylor's series ∑n=1∞fn(x0)n!x-x0n exist and…

Answered: (b) What are the singular points, if…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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(b.) Consider the ordinary differential equation in (t > 0) ty" – (t+1)y' + y = 0 Note that Y1(t) = et is a solution of this equation. (i). Write y(t) = v(t)e* and derive a differential equation v(t). Solution: • +(1 – ) : = 0 (ii). Solve the equation for v(t) you derive in (a). Solution. exp( )+ exp(-t)) + c2 v = (iii). Write out an expression for the general solution of the original ordinary differential equation. Solution: The general solution for y is y(t) = c1 ( )+cz exp( ). (c). Using the method of undetermined coefficients, find the particular solution of the following initial value problem: (a). y" + 4y' + 4y = 2te 24, y(0) = 1, y'(0) = –3 General Solutions: y(t) = c1 exp( +c2 exp(-2t) + 5 exp( Applying initial conditions c1 C2 Particular Solutions: y = exp( )-t exp( )+t3 exp(
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(b) What are the singular points, if any, of each of the following ordinary differential equations? (i) x(x – 1)y" + (3r – 1)y/ + y = 0. (ii) xy" + (x – 6)y' – 3y = 0 (iii) y" + (In x)y = 0