Which of the following statements regarding the assumptions of differential equations are correct?

1. The coefficients of the terms in a linear differential equation must be continuous functions.
2. The solutions to a linear ordinary differential equation can be expressed as a linear combination of independent solutions.
3. Nonlinear differential equations cannot have unique solutions, regardless of initial conditions.
4. The existence and uniqueness theorem states that if the function and its partial derivatives are continuous, a unique solution exists for the initial value problem.