Victor Camocho
math2250fall2011-2
WeBWorK assignment number Homework 9 is due : 10/27/2011 at 11:00pm MDT.
The
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for the course contains the syllabus, grading policy and other information.
This file is /conf/snippets/setHeader.pg you can use it as a model for creating files which introduce each problem set.
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4. (1 pt) Library/OSU/accelerated calculus and analytic geometry i-
1. (1 pt) Library/Rochester/setDiffEQ12HigherOrder/ur de 12 5.pg
Find y as a function of x if
000
00
/hmwk7/prob6.pg
Match the following differential equations with their solutions.
The symbols A, B, C in the solutions stand for arbitrary constants.
You must get all of the answers correct to receive credit.
0
y − 7y − y + 7y = 0,
y(0) = 7, y0 (0) = 7, y00 (0) = −41.
y(x) =
1.
2. (1 pt) Library/Rochester/setDiffEQ12HigherOrder/ur de 12 4.pg
Find y as a function of x if
2.
3.
y(4) − 8y000 + 16y00 = 0,
y(0) = 13,
y(x) =
y0 (0) = 4,
y00 (0) = 16,
4.
5.
A.
B.
C.
D.
E.
y000 (0) = 0.
3. (1 pt) hw9/p3.pg
Match the fourth order linear equations with their fundamental
solution sets. You may use Maple or Matlab to assist you in
factoring higher order polynomials.
5.
1.
2.
3.
4.
5.
6.
y(4) − 12y000 + 54y00 − 108y0 + 81 = 0
y(4) + 9y000 = 0
y(4) − y = 0
y(4) = 0
y(4) − 2y000 + 9y00 − 8y0 + 20 = 0
y(4) − 3y000 − 3y00 + 11y0 − 6y = 0
d2y
+ 16y = 0
dx2
dy
−2xy
dx = x2 −4y2
dy
d2y
+ 9y = 0
+ 6 dx
dx2
dy
=
8xy
dx
dy
2
2
dx + 9x y = 9x
y = A cos(4x) + B sin(4x)
y = Ae−3x + Bxe−3x
3
y = Ce−3x + 1
3yx2 − 4y3 = C
2
y = Ae4x
(1 pt) Library/Utah/AP Calculus I/set10 Differential Equations-
/q0.pg
Here are some initial value problems with obvious solutions, as
discussed in class. In all cases the solutions are functions of x.
All letters other than y and x denote constants.
The solution of
y0 = ky,
y(0) = A
is
A.
B.
C.
D.
E.
F.
e3t ,
y(x) =
The solution of
te3t , t 2 e3t , t 3 e3t
1, t, sin(3t), cos(3t)
et sin(2t), et cos(2t), cos(t), sin(t)
e3t , e−2t , et , tet
1, t, t 2 ,t 3
et , e−t , sin(t), cos(t)
y00 = k2 y,
.
y(1) = y(−1) = A
is
y(x) =
The solution of
y00 = k2 y,
1
.
y(1) = −y(−1) = A
is
y(x) =
The solution of
y00 = −k2 y,
.
y(0) = 1,
y0 (0) = 0
7. (1 pt) hw9/p7.pg
A body with mass 250 g is attached to the end of a spring that is
stretched 25cm by a force of 9N. At time t=0 the body is pulled
1m to the right, stretching the spring, and set in motion with an
initial velocity of 5m/s to the left.
y0 (0) = 1
(a) Find x(t) in the form C cos(ω0t − α).
x(t) =
is
y(x) =
The solution of
y00 = −k2 y,
.
y(0) = 0,
is
y(x) =
The solution of
y00 = −k2 y,
(b) What is the amplitude of motion?
.
y(0) = A,
y0 (0) = B
(c) What is the period of motion?
is
y(x) =
.
8. (1 pt) hw9/p8.pg
Suppose that the mass in a mass-spring-dashpot system with
m = 8, c = 5, k = 2 is set in motion with x(0) = 0 and
x0 (0) = 10.
6. (1 pt) Library/Dartmouth/setStewartCh10S1/problem 1.pg
For what positive values of k does the function y = sin(kt)
satisfy the differential equation y00 + 121y = 0?
(a) Find Find the position function x(t).
For what negative values of k does the function y = cos(kt)
satisfy the differential equation y00 + 121y = 0?
x(t) =
(b) How far does the mass move to the right before starting
back toward the origin?
c
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Team, Department of Mathematics, University of Rochester
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