To prove: The given system d x d t = x − 2 y , d y d t = 3 x − 4 y can be transformed to d u d t = − 2 u , d υ d t = − υ using change of variables x = 2 u + υ . y = 3 u + υ . The u -axis maps to the line y = 3 2 x and υ -axis maps to the line y = x .

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Answer 1

Question

Chapter 12.2, Problem 23E

To determine

To prove:

The given system dxdt=x−2y, dydt=3x−4y can be transformed to dudt=−2u,dυdt=−υ using change of variables x=2u+υ. y=3u+υ.

The u-axis maps to the line y=32x and υ-axis maps to the line y=x.

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Answer 2

Question

Chapter 12.2, Problem 23E

To determine

To prove:

The given system dxdt=x−2y, dydt=3x−4y can be transformed to dudt=−2u,dυdt=−υ using change of variables x=2u+υ. y=3u+υ.

The u-axis maps to the line y=32x and υ-axis maps to the line y=x.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 12.2, Problem 23E

To determine

To prove:

The given system dxdt=x−2y, dydt=3x−4y can be transformed to dudt=−2u,dυdt=−υ using change of variables x=2u+υ. y=3u+υ.

The u-axis maps to the line y=32x and υ-axis maps to the line y=x.

Expert Solution & Answer

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Check out a sample textbook solution

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Answer 4

Question

Chapter 12.2, Problem 23E

To determine

To prove:

The given system dxdt=x−2y, dydt=3x−4y can be transformed to dudt=−2u,dυdt=−υ using change of variables x=2u+υ. y=3u+υ.

The u-axis maps to the line y=32x and υ-axis maps to the line y=x.

Expert Solution & Answer

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Check out a sample textbook solution

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Answer 5

Chapter 12.2, Problem 23E

To determine

To prove:

The given system dxdt=x−2y, dydt=3x−4y can be transformed to dudt=−2u,dυdt=−υ using change of variables x=2u+υ. y=3u+υ.

The u-axis maps to the line y=32x and υ-axis maps to the line y=x.

Answer 6

Chapter 12.2, Problem 23E

To determine

To prove:

The given system dxdt=x−2y, dydt=3x−4y can be transformed to dudt=−2u,dυdt=−υ using change of variables x=2u+υ. y=3u+υ.

The u-axis maps to the line y=32x and υ-axis maps to the line y=x.

Answer 7

Chapter 12.2, Problem 23E

To determine

To prove:

The given system dxdt=x−2y, dydt=3x−4y can be transformed to dudt=−2u,dυdt=−υ using change of variables x=2u+υ. y=3u+υ.

The u-axis maps to the line y=32x and υ-axis maps to the line y=x.

Answer 8

Expert Solution & Answer

Answer 9

Expert Solution & Answer

Answer 10

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Answer 11

Ch. 12.2 - In Problem 16, classify the critical point at the...Ch. 12.2 - Prob. 2E Ch. 12.2 - Prob. 3E Ch. 12.2 - Prob. 4E Ch. 12.2 - Prob. 5E Ch. 12.2 - Prob. 6E Ch. 12.2 - Prob. 7E Ch. 12.2 - Prob. 8E Ch. 12.2 - Prob. 9E Ch. 12.2 - In Problem 712, find and classify the critical...

To prove: The given system d x d t = x − 2 y , d y d t = 3 x − 4 y can be transformed to d u d t = − 2 u , d υ d t = − υ using change of variables x = 2 u + υ . y = 3 u + υ . The u -axis maps to the line y = 3 2 x and υ -axis maps to the line y = x .

Solution Summary: The author proves that the given system dudt=-2u,.. upsilon -axis maps to the line

To prove:

The given system dxdt=x−2y, dydt=3x−4y can be transformed to dudt=−2u,dυdt=−υ using change of variables x=2u+υ. y=3u+υ.

The u-axis maps to the line y=32x and υ-axis maps to the line y=x.

Want to see the full answer?

Chapter 12 Solutions

To prove: The given system d x d t = x − 2 y , d y d t = 3 x − 4 y can be transformed to d u d t = − 2 u , d υ d t = − υ using change of variables x = 2 u + υ . y = 3 u + υ . The u -axis maps to the line y = 3 2 x and υ -axis maps to the line y = x .

Solution Summary: The author proves that the given system dudt=-2u,.. upsilon -axis maps to the line

To prove: The given system dxdt=x−2y, dydt=3x−4y can be transformed to dudt=−2u,dυdt=−υ using change of variables x=2u+υ. y=3u+υ. The u-axis maps to the line y=32x and υ-axis maps to the line y=x.

Want to see the full answer?

Chapter 12 Solutions

To prove:

The given system dxdt=x−2y, dydt=3x−4y can be transformed to dudt=−2u,dυdt=−υ using change of variables x=2u+υ. y=3u+υ.

The u-axis maps to the line y=32x and υ-axis maps to the line y=x.