- #1
JMeyer
- 1
- 0
Hello,
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(t0) = x0.
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.
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(t0) = x0.
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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