Nikita Sharma 2019W2 MATH 101 209
Assignment Homework 8 due 9/12/14 at 9pm
dy x 5. (1 point) Find the solution of the differential equation
1. (1 point) Solve the differential equation = .
dx 4y dy
(1) Find an implicit solution and put your answer in the fol- + y cos(x) = 3 cos(x)
dx
lowing form:
that satisfies the initial condition y(0) = 5.
= constant.
Answer: y=
Your answer should be a function of x.
(2) Find the equation of the solution through the point Correct Answers:
(x, y) = (1, 2).Your answer should be of the form y =
• 3 + 2*eˆ(-sin(x))
f (x).
dy 6y
6. (1 point) Solve the differential equation = , x>0
dx x
(3) Find the equation of the solution through the point .
(x, y) = (0, −4). Your answer should be of the form Answer: y(x) =
y = f (x).
Note: Use C as your constant and simplify it so it is not
Please click if you need help (formulas). negated or multiplied by a number in your solution.
Please click if you need help (equations). Correct Answers:
Correct Answers: • C*xˆ6
• yˆ2-(x/2)ˆ2 7. (1 point)
• y = sqrt((xˆ2+2ˆ4-1)/(2ˆ2)) Let A and k be positive constants.
• y = -[sqrt((x/2)ˆ2+16)] Which of the given functions is a solution to dydt = k(y − A)?
2. (1 point) Find an equation of the curve that satisfies Note: you have only two attempts to answer this question.
dy • A. y = A−1 +Ce−Akt
= 32yx7 • B. y = −A +Cekt
dx
• C. y = A +Cekt
and whose y-intercept is 3.
• D. y = −A +Ce−kt
y(x) = .
• E. y = A−1 +CeAkt
Correct Answers: • F. y = A +Ce−kt
• 3*exp(4*xˆ8 ) Solution:
SOLUTION
3. (1 point) We can find the correct answer by plugging the answers into
dy 10xy the differential equation to see which satisfies the equation.
Find the solution to the differential equation = which
dx (ln y)2 Here, dtd (A +Cekt ) = kCekt , so that, plugging in, we have
passes through the point (0,e). Express your answer as
ln y = kCekt = k(A +Cekt − A),
Correct Answers:
a true statement, so that the correct answer is y = A +Cekt .
• (10*(2+1)*x*x/2 + 1)ˆ(1/(2+1)) Correct Answers:
4. (1 point) Find the particular solution of the differential • C
equation
dy 8. (1 point) Find a formula for the general term an of the
= (x − 5)e−2y sequence (starting with a1 ):
dx
satisfying the initial condition y(5) = ln(5). 1 1 1 1
, , , ,...
6 12 18 24
y=
Your answer should be a function of x. an =
Correct Answers: Correct Answers:
• (1/2)*ln((x-5)ˆ2+5ˆ2) • 1/(6*n)
1
Assignment Homework 8 due 9/12/14 at 9pm
dy x 5. (1 point) Find the solution of the differential equation
1. (1 point) Solve the differential equation = .
dx 4y dy
(1) Find an implicit solution and put your answer in the fol- + y cos(x) = 3 cos(x)
dx
lowing form:
that satisfies the initial condition y(0) = 5.
= constant.
Answer: y=
Your answer should be a function of x.
(2) Find the equation of the solution through the point Correct Answers:
(x, y) = (1, 2).Your answer should be of the form y =
• 3 + 2*eˆ(-sin(x))
f (x).
dy 6y
6. (1 point) Solve the differential equation = , x>0
dx x
(3) Find the equation of the solution through the point .
(x, y) = (0, −4). Your answer should be of the form Answer: y(x) =
y = f (x).
Note: Use C as your constant and simplify it so it is not
Please click if you need help (formulas). negated or multiplied by a number in your solution.
Please click if you need help (equations). Correct Answers:
Correct Answers: • C*xˆ6
• yˆ2-(x/2)ˆ2 7. (1 point)
• y = sqrt((xˆ2+2ˆ4-1)/(2ˆ2)) Let A and k be positive constants.
• y = -[sqrt((x/2)ˆ2+16)] Which of the given functions is a solution to dydt = k(y − A)?
2. (1 point) Find an equation of the curve that satisfies Note: you have only two attempts to answer this question.
dy • A. y = A−1 +Ce−Akt
= 32yx7 • B. y = −A +Cekt
dx
• C. y = A +Cekt
and whose y-intercept is 3.
• D. y = −A +Ce−kt
y(x) = .
• E. y = A−1 +CeAkt
Correct Answers: • F. y = A +Ce−kt
• 3*exp(4*xˆ8 ) Solution:
SOLUTION
3. (1 point) We can find the correct answer by plugging the answers into
dy 10xy the differential equation to see which satisfies the equation.
Find the solution to the differential equation = which
dx (ln y)2 Here, dtd (A +Cekt ) = kCekt , so that, plugging in, we have
passes through the point (0,e). Express your answer as
ln y = kCekt = k(A +Cekt − A),
Correct Answers:
a true statement, so that the correct answer is y = A +Cekt .
• (10*(2+1)*x*x/2 + 1)ˆ(1/(2+1)) Correct Answers:
4. (1 point) Find the particular solution of the differential • C
equation
dy 8. (1 point) Find a formula for the general term an of the
= (x − 5)e−2y sequence (starting with a1 ):
dx
satisfying the initial condition y(5) = ln(5). 1 1 1 1
, , , ,...
6 12 18 24
y=
Your answer should be a function of x. an =
Correct Answers: Correct Answers:
• (1/2)*ln((x-5)ˆ2+5ˆ2) • 1/(6*n)
1
