Second Order Differential Equation

In summary, the conversation is about a problem in an advanced college physics class that involves a second order differential equation. The given constants are B, L, A, m, σ, and θ, and the goal is to express everything in terms of these constants, x, and t. The equation provided in the conversation is incorrect, and the correct equation is given instead. The next step is to integrate the equation with respect to t to find the velocity in terms of x and t.
  • #1
Axecutioner
32
0
This is from an advanced college physics class, and I'm only in a Calc 1 right now. I've finished the whole problem except for this last part, which deals with a second order differential equation, which I don't know how to do yet.

Homework Statement


Givens: B, L, A, m, σ, θ (all are constant)
From what I have below, I need to get everything in terms of the givens, x, and t

Homework Equations


I have reduced everything down to this:
[PLAIN]http://img718.imageshack.us/img718/513/phy.png
The first equation is from the problem, the second gets it in differential equation form.

The Attempt at a Solution


Like I said above, I've solved the whole problem except what I haven't learned how to do yet.


Thanks!
~Axe
 
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  • #2
Your differential equation isn't correct. It should be

[tex]\frac{B^2L^2\sigma A}{2L+2x}\frac{dx}{dt} = m\frac{dv}{dt} + mg \sin\theta[/tex]

You can integrate that with respect to t to find v in terms of x and t. Is that what you're solving for?
 

FAQ: Second Order Differential Equation

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 is typically represented in the form of y'' + p(x)y' + q(x)y = g(x), where y is the dependent variable, x is the independent variable, and p(x), q(x), and g(x) are functions of x.

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

The key difference between a first and second order differential equation is the highest order derivative involved. A first order differential equation involves only the first derivative of a function, while a second order differential equation involves the second derivative. This means that a second order differential equation is more complex and requires two initial conditions to be solved.

3. How are second order differential equations used in science?

Second order differential equations are used in many areas of science, including physics, engineering, and biology. They are used to model the behavior of systems that are influenced by multiple factors and are often used to predict future outcomes based on initial conditions and known variables.

4. What are some common techniques for solving second order differential equations?

Some common techniques for solving second order differential equations include separation of variables, substitution, and using an integrating factor. Other methods such as the Laplace transform and numerical methods like Euler's method can also be used.

5. Can all second order differential equations be solved analytically?

No, not all second order differential equations can be solved analytically. Some equations may be too complex or have no known solution. In these cases, numerical methods or approximations may be used to find a solution.

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