
Title: Existence and Uniqueness?

Series: Ordinary Differential Equations

YouTubeTitle: Ordinary Differential Equations 8  Existence and Uniqueness?

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Quiz: Test your knowledge

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Quiz Content
Q1: Consider the ordinary differential equation $\dot{x} = 3 x + 1$. Does a solution for the initial value problem with $x(0) = x_0$ always exist?
A1: Yes!
A2: No, never!
A3: Only for $x_0 \neq 0$.
Q2: Consider the ordinary differential equation $\dot{x} = v(x)$ with continuous $v$. Can it happen that you have two distinct solutions for the initial value problem with $x(0) = 0$.
A1: Yes, for some continuous functions $v$ this can happen.
A2: No, never!
A3: This can only happen for noncontinuous functions $v$.
Q3: Consider the ordinary differential equation $\dot{x} = 3 x + 1$. Can it happen that you have two distinct solutions for the initial value problem with $x(0) = 0$.
A1: Yes, one can have more solutions.
A2: No, this cannot happen for this example.
A3: One needs more information.