Math 257/316 Assignment 1 Solutions
Problem 1. Find the solution to the initial value problem for the ODE
dy
1+y
=
dx
1+x
for each of the initial conditions
(a) y(0) = 1,
(b) y(0) = 1,
(c) y(0) = 2
Th
M257/316 SolutionsAssignment 1
UBC M257/316 Resources (c) 2014 by Philip D. Loewen
1. (a) Find the general solution:
y + 6y + 13y = 0.
(b) Find all zeros of the function y, given
4y + 12y + 9y = 0,
(c
Trinity University
Digital Commons @ Trinity
Books and Monographs
12-2013
Elementary Differential Equations with Boundary
Value Problems
William F. Trench
Trinity University, [email protected]
Follo
Math 257/316 Assignment 7 Solutions
1. The concentration u(x, t) of a reactive chemical diusing in one dimension satises
0 < x < 2, t > 0
ut = uxx u,
u(0, t) = 1, u(2, t) = 1
.
u(x, 0) = 0
where the
Assignment 5
Due date: August 9, 2016
1. Solve the following heat equations with boundary conditions:
(a) ut = uxx , 0 < x < 1, t > 0,
u(0, t) = 0, u(1, t) = 0, t > 0,
u(x, 0) = x(1 x), 0 x 1.
(b) ut
Final Exam Guide
The cumulative final exam will be on Friday, December 18 from 12:0014:30 in ANGU 098. I will hold extra office hours before the exam, the exact
date will be announced later.
You will
Math 257/316, Homework 3
1. Consider the differential equation
P (x)y 00 + Q(x)y 0 + R(x)y = 0.
Let x = 0 be a regular singular point.
Then, show that the indicial equation for this differential equat
Math 257/316, Homework 5
Due March 6 IN CLASS
Please bring your homework to the section you are registered to
1. Find the full range Fourier series expansion of the functions;
f (x) = x for < x < ,
Math 257/316, Homework 4
Due February 27 IN CLASS
Please bring your homework to the section you are registered to
Please solve the following heat equations by first seperating variables and solving th
Math 257/316, Assignment 1: due in class September 23rd 2016
1. Compute all eigenvalues and eigenfunctions
of x + x =0, x (a) = 0, x(b) = 0 (assume
a < b). Hint: when > 0, then cos( (t a) and sin( (t
Math 257/316 Assignment 7, Due Wednesday Nov. 1 th in class
Note: The final Exam is on Thursday December 7 at 8:30.
Problem 1: (Old Exam Question) Solve the initial boundary value problem:
ut = uxx +
Math 257/316 Assignment 9 Supplemental Problems
Supplemental problems not to be handed in - solutions are provided.
Problem 1: Solve the following BVP in the rectangle cfw_(x, y) ; 0 x 1 , 0 y 1:
u +
Math 257/316 Assignment 8
Not to be handed in
Problem 1: Consider an infinite string subject to the initial condition
u(x, 0) =
x+1
1x
0
if 1 < x < 0
if 0 < x < 1
otherwise
ut (x, 0) = 0.
Sketch the
MATH 257/316 Assignment 6
Due: Wednesday, 25 th October in class
Problem 1: (Do Not hand in) Fourier Series and Parsevals Theorem
Let f o (x) be the odd periodic extension of period 2 of the function
Math 257/316 Assignment 7
Supplemental Examples: Not to be handed in - solutions are posted.
Problem 1: (A bar subject to a time dependent boundary condition
also Eg 22.2 in Lecture 22). Consider a ba
LECTURE 6: SINGULAR POWER SERIES NEAR A REGULAR SINGULAR POINT AND
BESSELS EQUATION
MINGFENG ZHAO
July 15, 2015
Series solutions near a regular singular points
Let x = a be a regular singular point of
LECTURE 1: REVIEW OF ORDINARY DIFFERENTIAL EQUATIONS
MINGFENG ZHAO
July 07, 2015
Separable dierential equations
A separable dierential equation has the form of:
y =
dy
= f (x)g(y).
dx
There are two ca