Sample Problems
1. How to use the separation of variable to solve a 1st order ODE?
2. When can we use the integration factor to solve a 1st order ODE?
3. How to use the integration factor to solve a homogeneous 1st order ODE? Will the solution identical to
that by the separation of variable?
4. How to use the Euler’s method to solve a 1st order ODE?
5. Why the midpoint method is a better choice than the Euler’s method?
6. What are the differences between the Euler’s method and higher order Runge-Kutta method?
7. Please use a graph with time in x-axis and h in y-axis to illustrate your understanding of different
numerical methods.
8. Please give an example in hydrology, geology, or other disciplinary that can be expressed by the 1st order
ODE.
9. Considering a lake where the precipitation, evapotranspiration, infiltration, and municipal water supply
are the dominant hydrological processes controlling the water balance. Use mass balance (or continuity
equation) to formulate this hydrological system into a 1st order ODE. Assume the infiltration can be
expressed by a linear reservoir model.