Let f : &reals; 2 → &reals; be a locally Lipschitz function. Consider the system of ODEs given by &xdot; 1 = sin(e x 2 ), &xdot; 2 = f(x 1 , x 2 ) with the initial condition (x 1 (0), x 2 (0)) = (1, 1). Which of the following statements is true?

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Mathematics · Ordinary Differential Equations

Let f : &reals; 2 → &reals; be a locally Lipschitz function. Consider the system of ODEs given by &xdot; 1 = sin(e x 2 ), &xdot; 2 = f(x 1 , x 2 ) with the initial condition (x 1 (0), x 2 (0)) = (1, 1). Which of the following statements is true?

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There exists a unique local solution around time 0

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Answer 1

There exists a unique local solution around time 0

Answer 2

There might not be any solution around time 0

Answer 3

There always exists a global solution defined in [0, ∞)

Answer 4

There is at most one local solution at time 0

Let f : &reals; 2 → &reals; be a locally Lipschitz function. Consider the system of ODEs given by &xdot; 1 = sin(e x 2 ), &xdot; 2 = f(x 1 , x 2 ) with the initial condition (x 1 (0), x 2 (0)) = (1, 1). Which of the following statements is true?

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Let f : &reals; 2 &rarr; &reals; be a locally Lipschitz function. Consider the system of ODEs given by &xdot; 1 = sin(e x 2 ), &xdot; 2 = f(x 1 , x 2 ) with the initial condition (x 1 (0), x 2 (0)) = (1, 1). Which of the following statements is true?

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Let f : &reals; 2 → &reals; be a locally Lipschitz function. Consider the system of ODEs given by &xdot; 1 = sin(e x 2 ), &xdot; 2 = f(x 1 , x 2 ) with the initial condition (x 1 (0), x 2 (0)) = (1, 1). Which of the following statements is true?