# Second order differential equation

• Mugged
In summary, a second order differential equation is a complex mathematical equation that involves the second derivative of a function. It differs from a first order differential equation in that it includes the second derivative and can represent more complicated relationships between variables. Real-life applications of second order differential equations include modeling systems in physics, engineering, economics, and biology. To solve a second order differential equation, various methods such as separation of variables, substitution, and using an integrating factor can be used. The initial conditions, or boundary conditions, are essential in finding a specific solution to the equation as they determine the constants of integration needed.
Mugged
Hi, i need help solving this equation:

$$y'' + 4y' + 4y = 0$$

any help is appreciated!

Mugged said:
Hi, i need help solving this equation:

$$y'' + 4y' + 4y = 0$$

any help is appreciated!

Here is a hint: For a 2nd order DE with constant coefficients, try using y=emx as a trial solution.

## 1. What is a second order differential equation?

A second order differential equation is a mathematical equation that involves the second derivative of a function. It represents the relationship between a function, its first derivative, and its second derivative.

## 2. How is a second order differential equation different from a first order differential equation?

A second order differential equation involves the second derivative of a function, while a first order differential equation only involves the first derivative. This means that a second order differential equation is more complex and can represent more complicated relationships between variables.

## 3. What are some real-life applications of second order differential equations?

Second order differential equations are commonly used in physics and engineering to model systems that involve acceleration, such as motion of objects, oscillations, and electrical circuits. They are also used in economics to model population growth and in biology to model population dynamics.

## 4. How do you solve a second order differential equation?

There are several methods for solving a second order differential equation, including separation of variables, substitution, and using an integrating factor. The specific method used will depend on the type of equation and initial conditions given.

## 5. What is the significance of the initial conditions in solving a second order differential equation?

The initial conditions, also known as boundary conditions, are the values of the function and its derivatives at a specific point. These conditions are necessary to find a specific solution to the differential equation, as they help determine the constants of integration that are needed in the solution.

• Calculus and Beyond Homework Help
Replies
7
Views
904
• Calculus and Beyond Homework Help
Replies
4
Views
517
• Calculus and Beyond Homework Help
Replies
6
Views
1K
• Calculus and Beyond Homework Help
Replies
8
Views
1K
• Calculus and Beyond Homework Help
Replies
7
Views
636
• Calculus and Beyond Homework Help
Replies
4
Views
2K
• Calculus and Beyond Homework Help
Replies
33
Views
3K
• Calculus and Beyond Homework Help
Replies
4
Views
1K
• Calculus and Beyond Homework Help
Replies
2
Views
492
• Calculus and Beyond Homework Help
Replies
9
Views
1K