What is differential equations?

Differential equation is that type of equation which contains derivatives in it. A differential equation can contain partial derivative or ordinary derivative. Depending on the derivative, the equation can be differential equation of first order, of second order, or of high order.

Various types of differential equations

There are several types of differential equations. Those differential equations which can be solved immediately making use of the derivatives from the table of derivatives are called elementary differential equations. The ordinary differential equations can be classified into 3 categories.

(1) Separable Differential Equations are the differential equations of first order and first degree whose variables are separable.

(2) Linear Differential Equations. A differential equation which has the following form: is known as a linear differential equation, as long as P and Q are only functions of x or constant, or only functions of y and constants.

(3) Homogeneous Differential Equations.

In mathematical terms, an exact differential equation is a specific type of ordinary differential equation used in physics and engineering. Talking about linear vs nonlinear differential equations, let's remind the definition for the line linear equations: We observe that the unknown function is of order 1, the same as the order of derivative. Our equation is equivalent with a linear algebraic system, and this is the reason our equation is called linear. However, there are cases when the unknown function is of higher order. In this situations the equation is no longer linear. Hence, the denomination of nonlinear differential equations. A system of differential equations represent a system which can be reduced to 2 or more differential equations.

Now that we found out what are systems of differential equations and what is differential equations, it's time we offer you some differential equations examples.

Some important differential equation examples:

Let's see some of the important differential equation problems:

Solve:

Solution:

The differential equation practice problems are very important because they help to improve your skills thereby making it easy to solve the problems on same.

Even you may find this difficult to believe, you have to know that the applications of differential equations are very useful for scientist, especially for physicists and chemists. There are a lot of physical quantities, and coefficients which are calculated using this type of equations.

 More topics in Differential Equations Derivatives of Logarithmic Functions Indefinite Integrals Ordinary Differential Equations Solving Differential Equations The Definite Integral The Method of Substitution Average Value of a Function
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