Order of a Differential Equation

In summary, the conversation discusses a differential equation with an integral and confusion about its order. It is clarified that the term "order" does not apply to this type of equation and the proposed method for solving it involves solving a related integra-differential equation and differentiating to find the original function.
  • #1
debrox
1
0
Hi. I'm reading a differential equation book to prime myself best for my signals and systems class I'm in, and I've ran into some confusion.

If I had a differential equation like so:

[tex]y'(t) + \int y(t)dt = f(t)[/tex] (1)

What would you say the order is? The definition says "the order of a differential equation is the highest derivative that appears in the equation."

Would I say it's a second order differential equation because:

[tex] h(t) = \int y(t)dt[/tex] (2)
meaning:
[tex] h''(t) = y'(t)[/tex] (3)
and substituting (2) and (3) into (1):
[tex]h''(t) + h(t) = f(t)[/tex] (4)

If asked to solve such a differential equation, would I first solve (4) and then differentiate h(t) to find y(t), the original function of t in question?
 
Last edited:
Physics news on Phys.org
  • #2
What you have initially is NOT a "differential equation". It is an "integra-differential equation" and the term "order" does not apply to it. Assuming f(t) is some reasonable function, then yes, the method you describe for solving it should work.
 

1. What is the order of a differential equation?

The order of a differential equation is the highest derivative present in the equation. It represents the number of times the dependent variable is differentiated with respect to the independent variable.

2. How is the order of a differential equation determined?

The order of a differential equation is determined by looking at the highest power of the derivative present in the equation. For example, if the equation contains only first derivatives, it is a first-order differential equation.

3. Why is the order of a differential equation important?

The order of a differential equation is important because it determines the number of initial conditions needed to find a unique solution. A first-order differential equation requires one initial condition, while a second-order differential equation requires two initial conditions.

4. Can the order of a differential equation change?

No, once the order of a differential equation is established, it cannot change. However, the order of a differential equation can be reduced through various mathematical techniques, such as substitution or integration.

5. How does the order of a differential equation affect its solution?

The order of a differential equation affects its solution by determining the complexity of the solution. Generally, higher-order differential equations have more complex solutions compared to lower-order ones. Additionally, the order also determines the number of constants present in the general solution of the equation.

Similar threads

  • Calculus and Beyond Homework Help
Replies
3
Views
515
  • Calculus and Beyond Homework Help
Replies
7
Views
133
  • Calculus and Beyond Homework Help
Replies
2
Views
221
  • Calculus and Beyond Homework Help
Replies
7
Views
642
  • Calculus and Beyond Homework Help
Replies
5
Views
846
  • Calculus and Beyond Homework Help
Replies
1
Views
663
  • Calculus and Beyond Homework Help
Replies
12
Views
1K
  • Calculus and Beyond Homework Help
Replies
4
Views
1K
  • Calculus and Beyond Homework Help
Replies
9
Views
657
  • Calculus and Beyond Homework Help
Replies
10
Views
868
Back
Top