Order the standard route from a physical situation to a prediction.

1. Identify the physical quantities and the forces acting
2. Write the governing differential equation, for instance F = m times the second derivative of x
3. Impose the initial conditions on position and velocity
4. Solve the equation exactly, or numerically if no closed form exists
5. Compare the resulting prediction with measurement

Differential equations sit at the centre of the route: everything before them is setting up, everything after is solving and testing. Initial conditions come before solving because they are what select one trajectory out of the whole family of solutions.