Ordinary Differential Equations 19

Ordinary Differential Equations 19 | Solution Space

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Күн бұрын

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Пікірлер: 13

@YouTube_username_not_found 2 күн бұрын

I'd like to be general and analyse the system for any functions A and b. Now here is the task: give a necessary and sufficient condition for the solvability of the system. If anyone will post an answer, please add a spoiler alert because I'd like to do this on my own.

@YouTube_username_not_found 2 күн бұрын

Spoiler Alert!!! Alright .. From a 1st look at the problem, I noticed that we have an equality between the derivative of x and A×x + b. By Darboux's theorem, we know that the derivative of any function must have the intermediate value property, thus A×x + b also have this property. And now I am out of ideas 😅