# Ordinary differential equations

I would like someone to introduce me to ODE and answer questions as they arise.

Â© BrainMass Inc. brainmass.com February 24, 2021, 2:12 pm ad1c9bdddfhttps://brainmass.com/math/ordinary-differential-equations/ordinary-differential-equations-integration-7388

#### Solution Preview

ODE is the part of calculus where both integration as well as differentiation are used..

simple equation:

dy/dx = f(x) : degree 1, order 1.

ORDER of eqn. : order of highest derivative

DEGREE of eqn.: index or power or raised to the highest order derivative

e.g. (dy/dx)^3 + (d^2y/dx^2)^2 : order 2, degree 2 (not 3)

Now,

e.g. eqn: dy/dx = sin(x)

solution=> dy = sin(x). dx

=> y = integration[sin(x)]dx = -cos(x) + const.

One step ahead:

dy/dx = f(x,y) : order 1, degree 1

e.g dy/dx = sin(x)/{sec(y).tan(y)}

=> sec(y).tan(y) dy = sin(x) dx

=> int[sec(y).tan(y)] dy = int[sin(x)] dx

=> sec(y) = ...

#### Solution Summary

This provides a brief introduction to ordinary differential equations. The ordinary differential equation integration is examined.