Learn Differential Equations with Free Lessons & Tips

Differential equation

are those equation which contain dependent ,independent variables,derivaives and partial derivatives

order:

the order of the differential equation is the order of the derivative

of the highest order occurring in the differential equation.

Degree:

The degree of a differential equation is the degree of the highest order differential coefficient appearing in it subject to the condition, that it can be expressed as a polynomial equation in derivatives.

General solution:

A solution in which the number of constants is equal to the order of

the equation is called the general solution of a differential

equation.

Particular Solution:

Particular solutions are derived from the general solution by assigning different values to the constants of a general solution.

Ordinary Differential Equation:

One depedent variable(Y) is dependent only on one independent variable(X).

Y is completely dependent on X.

Generally, Wife(Y) is completely dependent on Husband(X).

An ordinary differential equation (ODE) has only derivatives of one variable that is, it has no partial derivatives.

Here are a few examples of ODEs:

Y = f(X)

Partial Differential Equation:

One depedent variable(Y) is dependent at least two  variable(X) 

Generally WIfe & Childern & Grand pa/Ma is completely dependent on Father.

Wife, children & grand pa/ma are partially dependent on Father.

Y = F(X, Time, Temperature).

In contrast, a partial differential equation (PDE) has at least one partial derivative.

U = F(X, Y) U is partially dependent on X & Y.

V = f(X, T) U is partially dependent on X & T.

Here are a few examples of PDEs:

Industrial Example:

Mechanical property of Steel product = F(SoakingTime, Temperature, Phase transformation).

Mechanical property is partially dependent on soaking timransfore, temperature & phase transformation.