Solutions to Homework 8, Introduction to Dierential Equations, 3450:335-003, Spring 2009
Question 1. Use Laplace transform to solve the following initial value problem:
y + 5y 14y = 0, y (0) = 1, y (0
Review for the rst midterm, Introduction to Di. Eqs., 3450:335-003, Dr. Montero,
Spring 2009
Separable equations
A separable equation is an equation of the form
dy
= h(t)g(y),
dt
where h(t) depends on
Homework 7, Introduction to Dierential Equations, 3450:335-003, Spring 2009
Question 1. Consider the dierential equation
(x2 + 1)y 6y = 0,
and assume there is a solution of the form
k xk .
y ( x) =
k
Review for the third midterm, Introduction to Di. Eqs., 3450:335-003, Dr. Montero,
Spring 2009
Some useful facts regarding the Laplace transform.
For a function f (t) dened on [0, ), the Laplace trans
Solutions to Homework 3, Introduction to Dierential Equations, 3450:335-003, Dr.
Montero, Spring 2009
Problem 1. Find the determinant of the matrix
3 3 9
M = 0 2 5
0
0 4
Solution: The determinant is
Solutions to Homework 2, Introduction to Dierential Equations, 3450:335-003, Dr.
Montero, Spring 2009
Problem 1. The dierential equation below is exact. Find a function F(x,y) whose
level curves are s
Solutions to Homework 4, Introduction to Dierential Equations, 3450:335-003, Dr.
Montero, Spring 2009
Problem 1. Find the solution of the equation
9y 30y + 9y = 0
with the initial data
y (0) = 1 and y
Solutions to Homework 9, Introduction to Dierential Equations, 3450:335-003, Spring 2009
Question 1. Given that
L
cos(5t)
t
5
e s
= ,
s
nd the Laplace transform of
t
cos(5t).
Solution: Let us call
cos
Solutions to Homework 1, Introduction to Dierential Equations, 3450:335-003, Dr.
Montero, Spring 2009
problem 2. The problem says that the function
y (x) = ce2x + ex
solves the ODE
y + 2y = ex ,
and a
Midterm 3, Introduction to Dierential Equations, 3450:335-003, Spring 2009
Question 1. Find the Laplace transform Y (s) = L(y )(s) of the solution y (t) the following
initial value problem:
y (0) = 4,
Midterm 2, Introduction to Dierential Equations, 3450:335-003, Spring 2009
Question 1. Find the general solution of the equation
y 2y 35y = 0.
Solution: The polynomial associated to this equation is
2
Midterm 1, Introduction to Dierential Equations, 3450:335-003, Spring 2009
Question 1 (10 pts.) Find the solution of the dierential equation
y = 2(1 + y )t
that satises y (0) = 1.
Solution: This equat
Solutions to Homework 11, Introduction to Dierential Equations, 3450:335-003, Spring 2009
Question 1. Solve the system
dx
=
dt
12
3 6
x,
subject to the initial condition
3
5
x(0) =
.
Solution: We comp
Solutions to Homework 6, Introduction to Dierential Equations, 3450:335-003, Dr.
Montero, Spring 2009
Problem 1. Find a particular solution to
y + 6y + 9y =
25e3t
.
2(1 + t2 )
Solution: First we nd t
Solutions to Homework 5, Introduction to Dierential Equations, 3450:335-003, Dr.
Montero, Spring 2009
Problem 1. Find a particular solution to the dierential equation
y 4y = 48t3 .
Solution: First we