What is an nonlinear ordinary differential equation and give an example? What is an nonlinear ordinary differential equation and give an example?
And what is the difference between an linear ordinary differential equation and non-linear ordinary differential equation in formal way?
The second question seems more important to me, however, it seems too long to put in the title

here is an example of a nonlinear differential equation. $$\frac{dx}{dt} = x^2, x(0) = x_0 $$ you can separate the variables and solve find $$ x = \frac{x_0}{1- tx_0}$$
you can see that there are several things different from linear equations: principle of super position does not hold, (b) the solution may not exist for all time, (c) the singularity nay depend on the initial condition. most of the nonlinear differential equation have no closed form solutions. one usually linearizes about some known state and applied the method from the linear equations.
