To show that the system x ˙ = y , y ˙ = x cos y is reversible and sketch the phase portraits. Concept Introduction: The system of the form x ˙ = f ( x, y ) and y ˙ = g ( x, y ) is said to be reversible when f is odd in y and g is even in y. Another way is f (x,-y) = - f(x, y) and g (x,-y) = g(x, y) .

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Chapter 6.6, Problem 2E

Interpretation Introduction

Interpretation:

To show that the system x˙ = y , y˙ = x cos y is reversible and sketch the phase portraits.

Concept Introduction:

The system of the form x˙ = f(x, y) and y˙ = g(x, y) is said to be reversible when f is odd in y and g is even in y. Another way is f (x,-y) = - f(x, y) and g (x,-y) = g(x, y).

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