Math 5525. February 24, 2010. Midterm Exam 1. Problems and Solutions. Problem 1. Find the general solution of the equation dy xy 2 = xy. dx Solution. We have dy dy = x(y 2 + y ) = = x dx = dx y (y + 1) 1 1 y y+1 dy = x dx and y 0.
12 1 1 y+1 = ln |y | ln
Math 5525, Spring 2012
Homework 1
Due Friday February 3rd
1. Find the general solution of the following ODEs.
(a) y = 2x(y + x2 1)
(b) (2xe2xy + cos y )y + 2ye2xy = 0
(c) 2xyy + 3y 2 + 4x = 0
(d) xy = (y x)3 + y
(e) (x3 + x2 cos y + y 2 )y + 2x sin y + 3x
Math 5525: Introduction to Ordinary Differential Equations
Syllabus: Spring 2010
Class Times and Location: 2:30 pm 3:20 pm MWF, AmundH 240. Instructor: Mikhail Safonov, VinH 231, tel: 625-8571, email: safonov@math.umn.edu http:/www.math.umn.edu/safonov Of
Math 5525. April 14, 2010. Midterm Exam 2. Problems and Solutions. Problem 1. Find the general solution of the equation xy - (2x + 1)y + (x + 1)y = 0. Note that one of two linearly independent solutions is y1 (x) = ex . Solution. By Abel's formula, the Wr
Math 5525. May 11, 2010. Final Exam. Problems and Solutions. Problem 1 (10 points) Find the general solution of the problem dy y 2 - x2 x = + . dx xy y Solution. dy y 2 - x2 x y = + = , dx xy y x v= y x = v+x dv = v, dx dv = 0, dx v = C, y = Cx.
Problem 2
Math 5525: Spring 2010. Introduction to Ordinary Differential Equations: Homework #4. Problems and Solutions #1. Find the bounded continuous functions p1 (x), p2 (x), . . . , pn (x) with minimal possible n, such that the function x3 y(x) = sin x - x + 6 s
Math 5525: Spring 2010. Introduction to Ordinary Differential Equations: Homework #3. Problems and Solutions #1. Let y(x) be a solution of the problem y = sin y, y(0) = a R1 = (-, ),
which is defined on R1 . Show that y(x) is a monotone function on R1 , e
Math 5525: Spring 2010. Introduction to Ordinary Differential Equations: Homework #2. Problems and Solutions #1. Find the solution of the problem xy + 4y + x = 0. satisfying the initial condition y(1) = 0. Solution. The corresponding homogeneous equation
Math 5525: Spring 2010. Introduction to Ordinary Differential Equations Homework #4 (due on Wednesday, April 28). 100 points are divided between 5 problems, 20 points each. You can use without proof statements of Problems in the textbook. #1. Find the bou
Math 5525: Spring 2010. Introduction to Ordinary Differential Equations: Homework #3 (due on March 31). 100 points are divided between 6 problems. #1. (10 points). Let y(x) be a solution of the problem y = sin y, y(0) = a R1 = (-, ),
which is defined on R
Math 5525: Spring 2010. Introduction to Ordinary Differential Equations: Homework #2 (due on March 10). 100 points are divided between 8 problems. #1. (10 points). Find the solution of the problem xy + 4y + x = 0. satisfying the initial condition y(1) = 0
Math 5525: Spring 2010 Introduction to Ordinary Differential Equations: Homework #1 (due on February 10). 100 points are divided between 10 problems, 10 points each. #1. Find a second-order equation of the form a(x)y +b(x)y +c(x)y = 0, which has solutions
Math 5525: Spring 2010 Introduction to Ordinary Differential Equations
Information on Final Exam: Tuesday, May 11, 2010
Time and place: Tuesday, May 11, 10:30 am 12:30 pm, AmundH 240. There will be 8 problems. No books, no notes. Calculators are permitted