(a) Write the given equation as y 3 d y = 9 x 2 d x

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Answer 1

Question

Chapter 9.1, Problem 12E

To determine

(a)

Write the given equation as $y^{3} d y = 9 x^{2} d x$

To determine

(b)

To integrate both sides to obtain $\frac{y^{4}}{4} = 3 x^{3} + C$

To determine

(c)

To verify that $y = {(12 x^{3} + C)}^{1 / 4}$ is the general solution

To determine

(d)

To find the particular solution satisfying $y (1) = 2$

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A body of mass m at the top of a 100 m high tower is thrown vertically upward with an initial velocity of 10 m/s. Assume that the air resistance FD acting on the body is proportional to the velocity V, so that FD=kV. Taking g = 9.75 m/s2 and k/m = 5 s, determine: a) what height the body will reach at the top of the tower, b) how long it will take the body to touch the ground, and c) the velocity of the body when it touches the ground.

Answer 2

Question

Chapter 9.1, Problem 12E

To determine

(a)

Write the given equation as $y^{3} d y = 9 x^{2} d x$

To determine

(b)

To integrate both sides to obtain $\frac{y^{4}}{4} = 3 x^{3} + C$

To determine

(c)

To verify that $y = {(12 x^{3} + C)}^{1 / 4}$ is the general solution

To determine

(d)

To find the particular solution satisfying $y (1) = 2$

Expert Solution & Answer

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See solution

Answer 3

Question

Chapter 9.1, Problem 12E

To determine

(a)

Write the given equation as $y^{3} d y = 9 x^{2} d x$

To determine

(b)

To integrate both sides to obtain $\frac{y^{4}}{4} = 3 x^{3} + C$

To determine

(c)

To verify that $y = {(12 x^{3} + C)}^{1 / 4}$ is the general solution

To determine

(d)

To find the particular solution satisfying $y (1) = 2$

Expert Solution & Answer

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Answer 4

Question

Chapter 9.1, Problem 12E

To determine

(a)

Write the given equation as $y^{3} d y = 9 x^{2} d x$

To determine

(b)

To integrate both sides to obtain $\frac{y^{4}}{4} = 3 x^{3} + C$

To determine

(c)

To verify that $y = {(12 x^{3} + C)}^{1 / 4}$ is the general solution

To determine

(d)

To find the particular solution satisfying $y (1) = 2$

Expert Solution & Answer

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Answer 5

Chapter 9.1, Problem 12E

To determine

(a)

Write the given equation as $y^{3} d y = 9 x^{2} d x$

To determine

(b)

To integrate both sides to obtain $\frac{y^{4}}{4} = 3 x^{3} + C$

To determine

(c)

To verify that $y = {(12 x^{3} + C)}^{1 / 4}$ is the general solution

To determine

(d)

To find the particular solution satisfying $y (1) = 2$

Answer 6

Chapter 9.1, Problem 12E

To determine

(a)

Write the given equation as $y^{3} d y = 9 x^{2} d x$

Answer 7

Chapter 9.1, Problem 12E

To determine

(a)

Write the given equation as $y^{3} d y = 9 x^{2} d x$

Answer 8

To determine

(b)

To integrate both sides to obtain $\frac{y^{4}}{4} = 3 x^{3} + C$

Answer 9

To determine

(b)

To integrate both sides to obtain $\frac{y^{4}}{4} = 3 x^{3} + C$

Answer 10

To determine

(c)

To verify that $y = {(12 x^{3} + C)}^{1 / 4}$ is the general solution

Answer 11

To determine

(c)

To verify that $y = {(12 x^{3} + C)}^{1 / 4}$ is the general solution

Answer 12

To determine

(d)

To find the particular solution satisfying $y (1) = 2$

Answer 13

To determine

(d)

To find the particular solution satisfying $y (1) = 2$

Answer 14

Expert Solution & Answer

Answer 15

Expert Solution & Answer

Answer 16

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Answer 17

Ch. 9.1 - Prob. 1PQ Ch. 9.1 - Prob. 2PQ Ch. 9.1 - Prob. 3PQ Ch. 9.1 - Prob. 4PQ Ch. 9.1 - Prob. 5PQ Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E

(a) Write the given equation as y 3 d y = 9 x 2 d x

(a) Write the given equation as y3dy=9x2dx

(b) To integrate both sides to obtain y44=3x3+C

(c) To verify that y=(12x3+C)1/4 is the general solution

(d) To find the particular solution satisfying y(1)=2

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Chapter 9 Solutions

(a)

Write the given equation as $y^{3} d y = 9 x^{2} d x$

(b)

To integrate both sides to obtain $\frac{y^{4}}{4} = 3 x^{3} + C$

(c)

To verify that $y = {(12 x^{3} + C)}^{1 / 4}$ is the general solution

(d)

To find the particular solution satisfying $y (1) = 2$