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Differential equations can be used for many purposes, but ultimately they are simply a way of describing rates of change of variables in an equation relative to each other.
Many real world events can be modeled with differential equations.
For example, imagine that you are observing a cart rolling down a hill, and can measure it's displacement over time as being d = t2 + 3t + 4. Given that, you can calculate it's velocity at any given moment by taking the derivative of the same equation, as velocity is the rate of change of displacement:
d = t2 + 3t + 4
v = dd/dt
∴ v = 2t + 3
Similarly, because acceleration is the rate of change of velocity, you can use the same technique to calculate the rate at which the cart is accelerating:
v = 2t + 3
a = dv/dt
∴ a = 2
This is just one simple example of how differential equations can be used, but the number of applications are endless.
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What are the different Types of mathematical equations?
Algebraic equations, trigenometric equations, linear equations, geometric equations, partial differential equations, differential equations, integrals to name a few.
What is the classification of a system of equations?
The answer will depend on what kinds of equations: there are linear equations, polynomials of various orders, algebraic equations, trigonometric equations, exponential ones and logarithmic ones. There are single equations, systems of linear equations, systems of linear and non-linear equations. There are also differential equations which are classified by order and by degree. There are also partial differential equations.
Who invented the ordinary differential equations?
Olusola Akinyele
How do you do differential equations?
The website in the Related Link should be of some assistance.
What is differential equations as it relates to algebra?
It is an equation in which one of the terms is the instantaneous rate of change in one variable, with respect to another (ordinary differential equation). Higher order differential equations could contain rates of change in the rates of change (for example, acceleration is the rate of change in the rate of change of displacement with respect to time). There are also partial differential equations in which the rates of change are given in terms of two, or more, variables.
