Show that the initial value problem $\displaystyle x' = \frac{{x^3}{e^{t}}}{1+x^2} + {t^2}{\cos x}, x(0) = 1$ has a solution on $\displaystyle \mathbb{R}$.
I tried to use Picard's theorem, but to no avail I can't get any result.
Show that the initial value problem $\displaystyle x' = \frac{{x^3}{e^{t}}}{1+x^2} + {t^2}{\cos x}, x(0) = 1$ has a solution on $\displaystyle \mathbb{R}$.
I tried to use Picard's theorem, but to no avail I can't get any result.
I haven't watched the video myself, but you might want to look at this:
What is a Lipschitz condition? - YouTube