Spring 2011
Math 308-504
Quiz 11: Solutions
c Art Belmonte
Sun, 10/Apr
BB-431/5+ Solve the initial value problem = Ax, x (0) = x
x
0,
7
6 6
7
5 9 and x0 = 9 .
where A = 9
0 1 1
2
BB-421/11 Solve the initial value problem = Ax, x (0) = x
x
0,
1
0
3
2
0 and
Spring 2011
Math 308-504
Quiz 10B: Solutions
c Art Belmonte
Thu, 31/Mar
y (0) = 1,
t
y (t ) + 2
y (0) = 0.
Recognize the integral as a convolution.
y (t ) + 2 cos (t ) y (t ) = et
Graph the solution for 0 t 25, 2 y 2.
Take the Laplace transform of the d
Spring 2011
Math 308-504
Quiz 10A: Solutions
c Art Belmonte
Thu, 31/Mar
y (0) = 0,
t
y (t ) + 2
y (0) = 1.
Recognize the integral as a convolution.
y (t ) + 2 cos (t ) y (t ) = et
Graph the solution for 0 t 25, 2 y 2.
Take the Laplace transform of the d
Spring 2011
Math 308-504
Quiz 9A: Solutions
c Art Belmonte
Thu, 24/Mar
1. An undamped spring-mass system has a spring constant of
36 N/m. A 1 kg mass is attached to the spring. It is
suddenly set in motion from its equilibrium position at
time t = 0 by an
Spring 2011
Math 308-504
Quiz 8B: Solutions
c Art Belmonte
Wed, 16/Mar
1. An undamped spring-mass system has a spring constant of
36 N/m. A 1 kg mass is attached to the spring. It is
suddenly set in motion from its equilibrium position at
time t = 0 by an
Spring 2011
Math 308-504
Quiz 8A: Solutions
c Art Belmonte
Wed, 16/Mar
1. An undamped spring-mass system has a spring constant of
36 N/m. A 1 kg mass is attached to the spring. It is
suddenly set in motion from its equilibrium position at
time t = 0 by an
Spring 2011
Math 308-504
Quiz 7B: Solutions
c Art Belmonte
Wed, 09/Mar
1. Use the method of undetermined coefcients to nd a
general solution of the differential equation
y + y 2y = 4t + 6.
The characteristic equation of the corresponding
homogeneous equa
Spring 2011
Math 308-504
Quiz 7A: Solutions
c Art Belmonte
Wed, 09/Mar
1. Find a general solution of the differential equation
y 2y + 6y = 0.
The independent variable is t .
The characteristic equation is r2 2r + 6.
The quadratic formula gives
2 4 24
r=
Spring 2011
Math 308-504
Quiz 6B: Solutions
c Art Belmonte
Wed, 23/Feb
1. Solve the initial value problem (IVP)
6y 5y + y = 0,
y(0) = 1,
y (0) = 0.
The independent variable is t .
Determine roots of the characteristic equation.
6r2 5r + 1
=0
(3r 1) (2r 1
Spring 2011
Math 308-504
Quiz 6A: Solutions
c Art Belmonte
Wed, 23/Feb
1. Solve the initial value problem (IVP)
6y 5y + y = 0,
y(0) = 0,
y (0) = 1.
The independent variable is t .
Determine roots of the characteristic equation.
6r2 5r + 1
=0
(3r 1) (2r 1
Spring 2011
Math 308-504
Quiz 4A: Solutions
c Art Belmonte
Mon, 31/Jan
1. Consider the nonlinear differential equation
x2 y3 dx + x 1 + y2 d y = 0.
(a) Show that the equation is NOT exact.
With P = x2 y3 and Q = x 1 + y2 , we have
Py = 3x2 y2 and Qx = 1
Spring 2011
Math 308-504
Quiz 3A: Solutions
c Art Belmonte
Wed, 26/Jan
Bonus A
Obtain an explicit solution for the implicit solution in
Problem 1.
dy
= 2y2 + xy2 ,
dx
y (0) = 1.
Separate variables.
Antidifferentiate.
y
4
2
x
0
1
y1 = 2x + 2 x2 + C
Det
Spring 2011
Math 308-504
Quiz 2A: Solutions
c Art Belmonte
Tue, 18/Jan
1. Determine the values of the constant r for which the
differential equation
y + 5y + 6y = 0
has solutions of the form y = erx .
Compute derivatives.
y
= rerx
y
= r2 erx
Substitute
Spring 2011
Math 308-504
Quiz 1A: Solutions
c Art Belmonte
Tue, 18/Jan
1. Solve the initial value problem
dy
= (1 2x) y2 ,
dx
y (0) = 6
and state the domain on which the solution is valid,
consistent with the initial condition.
Separate the variables.
y2