Ordinary & Partial Differential Equation

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.