Types of Ordinary Differential Equation
There are four types of ordinary differential equations namely:
- Homogeneous and Non-homogeneous Differential Equations
- Linear and Non-linear Differential Equations
- Autonomous and Non-autonomous Differential Equations
Difference between Homogeneous and Non-homogeneous Differential Equation
Below is the difference between Homogeneous and Non-homogeneous Differential Equation.
| Homogeneous Differential Equations | Non-homogeneous Differential Equations |
|---|---|
| A differential equation in which all terms are of the same degree | A differential equation in which terms of different degrees are present |
| Example: d2y/dx2 + 2dy/dx + y = 0, y” – 3y’ + 2y = 0 | Example: d2y/dx2 + 3dy/dx + y = x2, y” – 3y’ + 2y = ex |
Linear and Non-linear Differential Equations
Below is the difference between Linear and Non-linear Differential Equations.
| Linear | Non-linear |
|---|---|
| A differential equation in which the dependent variable and its derivatives appear linearly | A differential equation in which the dependent variable and its derivatives appear non-linearly |
| Example: d2y/dx2 + 2dy/dx + 3y = 0, y’ + 2xy = 0 | Example: d2y/dx2 + sin(y) = 0, y” + y2 = 0 |
Difference between Autonomous and Non-autonomous Differential Equations
Below is the difference between Autonomous and Non-autonomous Differential Equation.
| Autonomous Differential Equations | Non-autonomous Differential Equations |
|---|---|
| A differential equation where the independent variable doesn’t explicitly appear | A differential equation where the independent variable explicitly appears |
| Example: dy/dt = y, y’ = y(1 – y) | Example: dy/dt = ty, y’ = y – x |
Ordinary Differential Equations
Ordinary Differential Equations(ODE) is the mathematical equation that describe how a function’s rate of change relates to its current state. It involves a single independent variable and its derivatives.
Ordinary Differential Equations
Let’s know more about Ordinary Differential Equations, it’s types, order and degree of Ordinary differential equation in detail below.
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