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I need to use the Gronwall inequality to discuss existence/uniqueness of the solution to the initial value problem:

x'(t)=xsin(tx) + t with initial condition x(t_{0}) = x_{0}.

I can convert this into integral form

[tex]x(t) = x_0 + \int\limits_{t_0}^{t} xsin(sx) + s ds[/tex]

Which of course can reduce to

[tex]x(t) = x_0 + \frac{t^2}{2} - \frac{t_0^2}{2} + \int\limits_{t_0}^{t} xsin(sx) ds[/tex]

But I'm unsure of how to progress from here. Also any links to other good places to study this material would help.

Thank you.

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# Using Gronwall Inequality to Prove Uniqueness/Existence

Can you offer guidance or do you also need help?

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