Diff. Eq. - Chapter 1 - Different Kinds of Differential Equations

 Chapter 1 - Different Kinds of Differential Equations 

The order of a differential equations refers to the highest derivative that is part of the differential equation.

> Order examples

A linear differential equations is expressed in the form:

A non-linear differential equation includes a coefficient of y instead of x, or a non-linear function of the dependent variable:

> Linear vs. Non-linear examples

A homogeneous differential equation is an equation is where the function (Let's say 'g(x)') is equal to zero. (g(x) = 0)

> First-order differential equations are homogeneous if there are in standard form, or if the first derivative is isolated.

> Second-order or higher differential equations are homogeneous if g(x) = 0, or in the form:

>> Homogenous diff. equations examples