Toronto Math Forum
Welcome,
Guest
. Please
login
or
register
.
1 Hour
1 Day
1 Week
1 Month
Forever
Login with username, password and session length
News:
Home
Help
Search
Calendar
Login
Register
Toronto Math Forum
»
MAT244--2018F
»
MAT244--Tests
»
Quiz-3
»
Q3 TUT 5102
« previous
next »
Print
Pages: [
1
]
Author
Topic: Q3 TUT 5102 (Read 4502 times)
Victor Ivrii
Administrator
Elder Member
Posts: 2607
Karma: 0
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.
$$
x^2y''+xy'+(x^2-\nu^2)y=0 \qquad\text{Bessel's equation}.
$$
Logged
Yiting Zhang
Jr. Member
Posts: 6
Karma: 8
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
»
Logged
Print
Pages: [
1
]
« previous
next »
Toronto Math Forum
»
MAT244--2018F
»
MAT244--Tests
»
Quiz-3
»
Q3 TUT 5102