1.In our world things change, and describing how they change often ends up as a Differential Equation:
Example: Rabbits!
The more rabbits we have the more baby rabbits we get. Then those rabbits grow up and have babies too! The population will grow faster and faster.
2.The use of differential equations to understand computer hardware belongs to applied physics or electrical engineering.
3.if you're working on something like computer vision, then there might well be differential equations involved, but it's certainly possible to be a computer scientist without knowing much about differential equations
4.If you develop a computer programme to predict future values, especially on engineering quantities, you will almost certainly use differential equations as part of your predictive algorithms in your tool kit.
5.In a simple video game involving a jumping motion, a differential equation is used to model the velocity of a character after the command is given to return them to the ground in a simulated gravitational field.
6.We see PDEs everywhere. More or less every phenomena be it physical, chemical or even biological can be represented in terms PDEs. Be it the behavior of waves, be it the flow of fluids or be it even a chemical reaction almost everything can be represented in terms of PDEs.
7.Using computers, especially embedded systems, in process control.
An example might be in brewing beer or in any other fermentation process, where you have to control the concentration of chemicals in solution. In olden times, analog computers were used for this, but nowadays it's pretty much all dynamic