Differential equation questions I am studying differential equations of order $1$ and $2$ and I had these questions on my mind:
1. Is it true that every differential equation has infinitely many solutions if there are no initial conditions specified?
2. Is it true or false that the solution of every $2$nd order differential equation always has $2$ independent constants?
Thank you for helping me out :)

For linear DEs, those two facts are always true. That is great, because you'll be working with linear DEs 99% of the time.
Non-linear DE's do not behave as nicely, and may not adhere to those rules. 
