Victor Camocho
math2250fall2011-2
WeBWorK assignment number Homework 10 is due : 11/03/2011 at 11:00pm MDT.
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5.
(1 pt) Library/Utah/Calculus II/set14 Differential Equations/set14 pr2.pg
1. (1 pt) hw10/p1.pg
Solve the initial value problem
Use the method of undetermined coefficients to solve the following differential equation:
dy
+ 2y = 25 sin(t) + 15 cos(t)
dt
with y(0) = 6.
y=
y00 + 6y0 + 9y = 2e−x
Answer: y(x) =
+C2
.
.
NOTE: The order of your answers is important in this problem. For example, webwork may expect the answer ”A+B” but
the answer you give is ”B+A”. Both answers are correct but
webwork will only accept the former.
2. (1 pt) Library/274/Lin1stord/prob12.pg
Solve the initial value problem
dy
− y = 9et + 14e3t
dt
with y(0) = 4.
y=
6.
(1 pt) Library/Utah/Calculus II/set14 Differential Equations/set14 pr1.pg
Use the method of undetermined coefficients to solve the following differential equation:
.
y00 + y0 = 4x
3. (1 pt) Library/Rochester/setDiffEQ12HigherOrder/ur de 12 8.pg
Find y as a function of x if
Answer: y(x) =
+C2
.
y(4) − 8y000 + 16y00 = −288e−2x ,
y(0) = 0,
y(x) =
y0 (0) = 9,
y00 (0) = 8,
+C1
+C1
NOTE: The order of your answers is important in this problem. For example, webwork may expect the answer ”A+B” but
the answer you give is ”B+A”. Both answers are correct but
webwork will only accept the former.
y000 (0) = 16.
4. (1 pt) Library/Rochester/setDiffEQ12HigherOrder/ur de 12 7.pg
Find y as a function of x if
7.
(1 pt) Library/Utah/Calculus II/set14 Differential Equations-
/set14 pr11.pg
Solve the following differential equation:
y000 − 9y00 + 18y0 = 20ex ,
y(0) = 19,
y(x) =
y0 (0) = 28,
y00 + 4y = sin3 x
y00 (0) = 16.
Answer: y(x) =
+C2
.
1
+C1
xtr (t) = c1 ·
8. (1 pt) hw10/p9.pg
Consider the damped forced oscillation system having the governing equation
+ c1 ·
(b) What is the amplitude of the stable periodic solution of
the system (NOTE: Your answer should be in terms of ω)?
Amplitude =
mx00 + cx0 + kx = F0 cos(ωt)
where m = 1, c = 6, k = 10, F0 = 10.
(c) At what value of ω does resonance occur?
ω=
(a) What is the general form of the transient solution of the
system?
c
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Team, Department of Mathematics, University of Rochester
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