Math Tutoring on Introduction to Differential Equations
A Differential Equation is an equation that contains an unknown function and its derivative.
To solve a Differential Equation, we want to determine an equation that satisfies the Derivative Equation. This will require Integration.
When solving a Differential Equation in the form , it is helpful to rewrite the equation in Differential Form. Then we can integrate both sides of the equation.
Types of Differential Equations:
1. Ordinary Differential Equations (ODE) – An Ordinary Differential Equation contains only Ordinary Derivative with respect to one Independent Variable.
2. Partial Differential Equations (PDE) – A Partial Differential Equation contains Partial Derivatives with respect to two or more Independent Variables.
The Order of a Differential Equation (ODE or PDE) – The Order of a Differential Equation is the Order of the highest derivative in the equation.
Linear and Nonlinear Differential Equations:
1. A Linear Differential Equation can be written in the form:
Note that –
· The Dependent Variable and all of its derivatives are always to the first power.
· There are no products of the function ‘y’ and its derivatives.
· The coefficients can be zero, constants, or functions of ‘t’.
2. A Nonlinear Differential Equation is a Differential Equation that is NOT linear.
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1. What is Differential Equations? How to solve it?
2. What are the Ordinary and Partial Differential Equations?
3. What is Linear Differential Equation? State some properties of it.
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