The given blank or answer true or false.

Question

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Answer 1

Question

Chapter 11, Problem 1CR

To determine

To fill: The given blank or answer true or false.

Expert Solution & Answer

Answer to Problem 1CR

The given differential equation can be written as plane autonomous system. So, the statement is true.

Explanation of Solution

The given statement is “The second-order differential equation $x″+f(x′)+g(x)=0$ can be written as a plane autonomous system.”

Now, assume that $x′=y$ . (1)

So the given differential equation becomes

$x″+f(x′)+g(x)=0y′+f(y)+g(x)=0$

Which on further solving gives,

$y′=−[f(y)+g(x)]$ . (2)

So, the given differential equation can be written as

$x′=y$ and $y′=−[f(y)+g(x)]$

Thus, it can be written as a plane autonomous system.

Hence, the given differential equation can be written as plane autonomous system. So, the statement is true.

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Answer 2

Question

Chapter 11, Problem 1CR

To determine

To fill: The given blank or answer true or false.

Expert Solution & Answer

Answer to Problem 1CR

The given differential equation can be written as plane autonomous system. So, the statement is true.

Explanation of Solution

The given statement is “The second-order differential equation $x″+f(x′)+g(x)=0$ can be written as a plane autonomous system.”

Now, assume that $x′=y$ . (1)

So the given differential equation becomes

$x″+f(x′)+g(x)=0y′+f(y)+g(x)=0$

Which on further solving gives,

$y′=−[f(y)+g(x)]$ . (2)

So, the given differential equation can be written as

$x′=y$ and $y′=−[f(y)+g(x)]$

Thus, it can be written as a plane autonomous system.

Hence, the given differential equation can be written as plane autonomous system. So, the statement is true.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Question

Chapter 11, Problem 1CR

To determine

To fill: The given blank or answer true or false.

Expert Solution & Answer

Answer to Problem 1CR

The given differential equation can be written as plane autonomous system. So, the statement is true.

Explanation of Solution

The given statement is “The second-order differential equation $x″+f(x′)+g(x)=0$ can be written as a plane autonomous system.”

Now, assume that $x′=y$ . (1)

So the given differential equation becomes

$x″+f(x′)+g(x)=0y′+f(y)+g(x)=0$

Which on further solving gives,

$y′=−[f(y)+g(x)]$ . (2)

So, the given differential equation can be written as

$x′=y$ and $y′=−[f(y)+g(x)]$

Thus, it can be written as a plane autonomous system.

Hence, the given differential equation can be written as plane autonomous system. So, the statement is true.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Chapter 11, Problem 1CR

To determine

To fill: The given blank or answer true or false.

Expert Solution & Answer

Answer to Problem 1CR

The given differential equation can be written as plane autonomous system. So, the statement is true.

Explanation of Solution

The given statement is “The second-order differential equation $x″+f(x′)+g(x)=0$ can be written as a plane autonomous system.”

Now, assume that $x′=y$ . (1)

So the given differential equation becomes

$x″+f(x′)+g(x)=0y′+f(y)+g(x)=0$

Which on further solving gives,

$y′=−[f(y)+g(x)]$ . (2)

So, the given differential equation can be written as

$x′=y$ and $y′=−[f(y)+g(x)]$

Thus, it can be written as a plane autonomous system.

Hence, the given differential equation can be written as plane autonomous system. So, the statement is true.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 11, Problem 1CR

To determine

To fill: The given blank or answer true or false.

Expert Solution & Answer

Answer to Problem 1CR

The given differential equation can be written as plane autonomous system. So, the statement is true.

Explanation of Solution

The given statement is “The second-order differential equation $x″+f(x′)+g(x)=0$ can be written as a plane autonomous system.”

Now, assume that $x′=y$ . (1)

So the given differential equation becomes

$x″+f(x′)+g(x)=0y′+f(y)+g(x)=0$

Which on further solving gives,

$y′=−[f(y)+g(x)]$ . (2)

So, the given differential equation can be written as

$x′=y$ and $y′=−[f(y)+g(x)]$

Thus, it can be written as a plane autonomous system.

Hence, the given differential equation can be written as plane autonomous system. So, the statement is true.

Answer 6

Chapter 11, Problem 1CR

To determine

To fill: The given blank or answer true or false.

Expert Solution & Answer

Answer to Problem 1CR

The given differential equation can be written as plane autonomous system. So, the statement is true.

Explanation of Solution

The given statement is “The second-order differential equation $x″+f(x′)+g(x)=0$ can be written as a plane autonomous system.”

Now, assume that $x′=y$ . (1)

So the given differential equation becomes

$x″+f(x′)+g(x)=0y′+f(y)+g(x)=0$

Which on further solving gives,

$y′=−[f(y)+g(x)]$ . (2)

So, the given differential equation can be written as

$x′=y$ and $y′=−[f(y)+g(x)]$

Thus, it can be written as a plane autonomous system.

Hence, the given differential equation can be written as plane autonomous system. So, the statement is true.

Answer 7

Chapter 11, Problem 1CR

To determine

To fill: The given blank or answer true or false.

Answer 8

Expert Solution & Answer

Answer to Problem 1CR

The given differential equation can be written as plane autonomous system. So, the statement is true.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Explanation of Solution

The given statement is “The second-order differential equation $x″+f(x′)+g(x)=0$ can be written as a plane autonomous system.”

Now, assume that $x′=y$ . (1)

So the given differential equation becomes

$x″+f(x′)+g(x)=0y′+f(y)+g(x)=0$

Which on further solving gives,

$y′=−[f(y)+g(x)]$ . (2)

So, the given differential equation can be written as

$x′=y$ and $y′=−[f(y)+g(x)]$

Thus, it can be written as a plane autonomous system.

Hence, the given differential equation can be written as plane autonomous system. So, the statement is true.

Answer 12

Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E Ch. 11.1 - Prob. 9E Ch. 11.1 - Prob. 10E

The given blank or answer true or false.

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To fill: The given blank or answer true or false.

Answer to Problem 1CR

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