Why do initial value problems for x' = ax have exactly one solution?

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Why do basic initial value problems have exactly one solution? This video discusses the uniqueness of solutions and explains why the exponential function is the only solution to the basic initial value problem for x' = ax.
  1. Dr Chris Tisdell
  2. math
  3. Chris Tisdell
  4. initial value problem
  5. differential equations
  6. linear differential equation
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Комментарии
Автор

Chris, you're the man, many thanks

mcgarybreik
Автор

Please do a similar video for second-order ODEs.

relikep
Автор

The fact that u(t) is a constant multiple of v(t) and vice versa shows that all (homogeneous) solutions (of x'-ax ) belong to a one-dimensional vector space. Is the term vector space correct in this context?

AlqGo