Victor Camocho
math2250fall2011-2
WeBWorK assignment number Homework 1 is due : 08/25/2011 at 11:00pm MDT.
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3. Given that y(x) = x2 + C solves y0 = 2x, find value of C
that satisfies the initial condition y(0) = 3
Use substitution to determine whether each function satisfies
the given differential equation. Enter ”T” if the statement is true
and ”F” if the statement is false.
1.
C=
y(x) = 8e−x solves y0 + 2y = 0.
2.
y(x) = 4 cos(7x) solves y00 + 7y = 0.
3.
y(x) = −2 cos(6x) + 5 sin(6x) solves y00 + 36y = 0.
4.
y(x) = 6e−x − 2e−2x solves y00 + 3y0 + 2y = 0.
5.
y0 (x) = ex solves y0 = 2xy.
6.
y(x) = 5x4 + 6x2 solves y0 = x5 + 2x3 + 4.
Suppose the velocity, v of a motorboat coasting in water satisfies the differential equations dv/dt = kv2 . The initial speed
of the motor boat is 10 meters per second, and the velocity is
decreasing at a rate of 1 meters per second squared when v = 5
m/s. How long does it take for the velocity of the boat to decrease to 91 m/s?
2
seconds.
Answer =
4. (1 pt) Library/274/Lin1stord/prob1.pg
Find the particular solution of the differential equation
dy
+ 7y = 5
dx
satisfying the initial condition y(0) = 0.
Answer: y =
.
Your answer should be a function of x.
5. (1 pt) Library/Michigan/Chap11Sec4/Q37.pg
Solve the differential equation
dR
= a(R2 + 9).
dx
Assume a is a non-zero constant, and use C for any constant of
integration that you may have in your answer.
R=
6. (1 pt) Library/Michigan/Chap11Sec4/Q23.pg
Find the solution to the differential equation
dy
= y2 (6 + t),
dt
y = 3 when t = 1.
y=
In each problem you are given a general solution to a differential equation, as well as an initial value. Find the value of C
that satisfies the initial condition in each case.
1. Given that y(x) = Cex solves y0 − y = 0, find value of C
that satisfies the initial condition y(0) = 7
C=
2. Given that y(x) = C cos(2x) solves y00 + 4y = 0, find value
of C that satisfies the initial condition y(0) = 6
C=
1
Time =
Speed =
On the planet Gzyx, a ball dropped from a height of 20 ft
hits the ground in 2 seconds. If the ball is dropped from a 800
ft building on Gzyx, how long will it take the ball to hit the
ground? At what speed will it hit the ground?
seconds
feet per second
NOTE: You are asked for a speed, not a velocity, so your answer
should be positive.
c
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Team, Department of Mathematics, University of Rochester
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