Question : i really need it...
Answer : Is this a question related to how to calculate separable differential equations? (Links are shown below for separable equations).
I will describe a very commonly found application of a separable first order differential equation.
This equation is applied in the growth/death rate of bacteria in biology, elimination of drugs in pharmacology, the continuous compounding of interest in economics, the half-life of a radioactive substance in physics, Newton's law of cooling (dT/dt = -r deltaT) in themodynamics, electrical relationships (V = Ldi/dt, I = CdVdt) in electrical engineering and many other phenomena are described by this one simple separable differential equation...
dy / dt = ky
1/y dy = k dt
integrating both sides yields
ln y = kt + c
y = e^(kt + c)
y = e^c e^kt
if A = e^c then
y = Ae^kt
Question : Please, Please, Support your opinion with examples.
Answer : The famous partial differential equation is the wave or Harmonic equation in physics. Then there is the Navier-Stokes equation in fluid mechanics. Just about any situation with multiple variables can be modeled with some partial differential equations. The problem is not so much as how the partial derivatives arise, but how to solve it.
What you learn in a partial differential equation class is not how it is actually solved in real-life. They only give you the simple cases. In real-life engineering, you have software programs using numerical techniques like finite differences to solve the partial derivative problems.
For example, the space shuttle foam problem during lift-off can be modeled with the Navier-Stokes partial differential equation. I believe it has 7 variables. If you leave all 7 variables unconstrained fluid flow over the shuttle structure, then it will probably require a few parallel supercomputing servers to crunch the numbers to look at all the different possibi..
Question : Can you give me some application of differential equation in computer science?
Answer : * In a typical algorithms book, you will not encounter a single differential equation. This is because differential equations work on continuous domains while the classic computer science algorithms are for discrete domains.
* On the other hand, if you consider numerical analysis as computer science, then differential equations is a HUGE field in that area.