Differential equation (2nd order)

Thread starter gomes.
Start date Nov 24, 2010
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2nd order Differential Differential equation

In summary, a second-order differential equation is a mathematical equation involving the second derivative of a function that is used to describe changes over time. The main difference between a first-order and second-order differential equation is the highest order of derivative involved. To solve a second-order differential equation, a general solution must be found and initial or boundary conditions can help find a particular solution. Second-order differential equations have various real-world applications, including modeling motion, describing electrical circuits, and predicting population growth. These equations can have multiple solutions due to arbitrary constants in the general solution.

Nov 24, 2010

gomes.

I seem to get the correct answer, but when i check my answer on wolfram, there is a 3C(2) instead of just C(2), am I doing something wrong or it doesn't matter if it is a 3C or C?

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Nov 24, 2010

rock.freak667

Homework Helper

Nope, because 3C is just another constant c. It really does not matter. Wolfram just does not account for things like that.

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, usually written in the form y'' = f(x,y,y'). It is used to describe how a system or process changes over time.

2. What is the difference between a first-order and a second-order differential equation?

The main difference between a first-order and a second-order differential equation is the highest order of derivative involved. A first-order differential equation involves the first derivative of a function, while a second-order differential equation involves the second derivative.

3. How do you solve a second-order differential equation?

To solve a second-order differential equation, you need to find a general solution that satisfies the equation. This can be done by using methods such as separation of variables, substitution, or using an integrating factor. Then, you can use initial or boundary conditions to find a particular solution.

4. What are some real-world applications of second-order differential equations?

Second-order differential equations are used in many fields of science, such as physics, engineering, and economics. They can be used to model the motion of objects, describe the behavior of electrical circuits, and predict population growth, among other things.

5. Can a second-order differential equation have more than one solution?

Yes, a second-order differential equation can have an infinite number of solutions. This is because when solving the equation, we usually obtain a general solution that contains arbitrary constants. These constants can take on different values, resulting in different solutions.