Author Topic: Q3 TUT 5102  (Read 907 times)

Victor Ivrii

  • Administrator
  • Elder Member
  • *****
  • Posts: 2511
  • Karma: 0
    • View Profile
    • Personal website of Victor Ivrii
Q3 TUT 5102
« on: October 12, 2018, 06:10:07 PM »
Find the Wronskian of two solutions of the given differential equation without solving the equation.
$$
x^2y''+xy'+(x^2-\nu^2)y=0 \qquad\text{Bessel's equation}.
$$

Yiting Zhang

  • Jr. Member
  • **
  • Posts: 6
  • Karma: 8
    • View Profile
Re: Q3 TUT 5102
« Reply #1 on: October 12, 2018, 06:36:23 PM »
$$y'' + \frac{x}{x^2}y' + \frac{x^2-v^2}{x^2}y = 0$$
$$W = ce^{-\int p(t)dt}$$
$$p(t) = \frac{1}{x}$$
$$-\int p(t)dt = -\ln{x}$$
$$W = ce^{-\ln{x}} = ce^{\ln{\frac{1}{x}}} = \frac{c}{x}$$
« Last Edit: October 12, 2018, 07:50:39 PM by Victor Ivrii »