# Tag Info

Accepted

### How to show there exists a smooth local frame $(\tilde{X_1},\cdots,\tilde{X_n})$ on some neighborhood of $A$ such that $\tilde{X_i}|_A=X_i$?

From J. M. Lee's book "Introduction to smooth manifolds" we have the next proposition: 10.12 Let $\pi:E\to M$ be a (smooth) vector bundle. Let $C$ be a closed subset of $M$ and $s:C\to E$ a (...
Accepted

### Behaviour of solution of differential equation at infinity

It does go to $+\infty$, but as $x$ approaches a finite value, namely $\ln(2)$.
### Prove that $\gamma$ is constant iff $\gamma′(t) = 0$ for all $t \in J$ if there is always an interval containing $t$ in which $\gamma$ is const
Your argument for $\implies$ looks fine. For $\impliedby$, I agree that we should use part (a), and I also like the fact that you're thinking about how $\gamma$ looks in a chart. Here's a way to ...
We could have $b_1=0$, and then $b_2$ can be whatever it wants. For a less trivial example, you could pick $b_1$ to be a vector field that "rotates" around the origin of the Euclidean plane (...