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Express the 2nd order ODE

$$\begin{align}\mathrm d_t^2 u:=\frac{\mathrm d^2 u}{\mathrm dt^2}&=\sin(u)+\cos(\omega t)\qquad \omega \in \mathbb Z /\{0\} \\u(0)&=a\\\mathrm d_t u(0)&=b\end{align}$$

as a system of 1st order ODEs and verify there exists a global solution by invoking the global existence and uniqueness theorems.

I'm not sure how to express second order ODEs as first order ODEs, any tips?

  • 2
    Make a new variable, $v=\dfrac{\mathrm du}{\mathrm dt}$...2011-10-09
  • 0
    How do you show there exists a global solution byt invoking the theorem? Theorem states: An IVP has a unique solution if the function f is continuous with respect to the 1st variable and Lipshitz continuous with respect to the 2nd variable.2012-09-27

2 Answers 2