<human>:  Why do we need to solve PDEs in order to solve ODEs?
<bot>: The reason is that ODEs are linear, while PDEs are nonlinear. If you want to solve an ODE, you can use a numerical method to approximate the solution. For example, Euler’s method is a very simple method that can be used to approximate the solution to a first-order ODE. However, this method is only valid if the initial condition is smooth, which is not the case for many types of ODEs.