• Title: Existence and Uniqueness?

  • Series: Ordinary Differential Equations

  • YouTube-Title: Ordinary Differential Equations 8 | Existence and Uniqueness?

  • Bright video: https://youtu.be/x3LTrFWr9R4

  • Dark video: https://youtu.be/NE9OlTtwgnQ

  • Quiz: Test your knowledge

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  • Subtitle on GitHub: ode08_sub_eng.srt missing

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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 non-continuous 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.

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