Yet another integral curve problem. The vector field this time is
$X_{(x,y)} = \dfrac{\partial}{\partial x} + x \dfrac{\partial}{\partial y}$.
So, using what I learned from my last post, I should solve
$\dot{x} = 1$ and $\dot{y} = x$. At least this is what I think. And the solution would be $c(t) = (x(t),y(t))$. This is a really stupid question, but how do I solve that system? At least for $\dot{y}$. If my thinking is wrong, please correct me as needed.
Thanks again! I'm preparing for an upcoming test and working problems from "An Introduction to Manifolds" by Tu. If anyone is curious, this is problem 14.5.