Differential Equation: 1st-Order in Time, 2nd-Order in Space

In summary, the order of a differential equation is determined by the highest derivative present, regardless of the variable it is with respect to. In this case, the given equation is a second order partial differential equation (PDE). However, when it comes to solving the PDE, the highest order is the only relevant factor. Therefore, the equation can be classified as either first order in both time and space, or second order in both.
  • #1
saravanan13
56
0
what is the order of differential equation which contains first order in time and second order in space derivative?
 
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  • #2
it will be the order of the highest derivative (doesn't matter in respect to what variable).
In your case, it's a second order pde
 
  • #3
Although it would also be perfectly acceptable to say "The differential equation is of second order in x and first order in t".
 
  • #4
It is a more specific classification

But in respect to how you solve the PDE, it's only important what's the highest order.

In this matter, how would you classify [tex]u_{xt}+blabla=0[/tex], first order in time and space, or second-order in both?
 

1. What is a differential equation?

A differential equation is a mathematical equation that relates a function with its derivatives. It describes how a function changes over time or space.

2. What is the difference between 1st-order and 2nd-order differential equations?

A 1st-order differential equation involves only the first derivative of a function, while a 2nd-order differential equation involves the second derivative. This means that a 1st-order equation describes how a function changes over time, while a 2nd-order equation describes how a function changes over both time and space.

3. What does it mean for a differential equation to be 1st-order in time and 2nd-order in space?

This means that the equation involves both the first derivative with respect to time and the second derivative with respect to space. It describes how a function changes over both time and space simultaneously.

4. What are some real-world applications of 1st-order in time and 2nd-order in space differential equations?

1st-order in time and 2nd-order in space differential equations are commonly used in physics and engineering to describe the motion of objects, such as the movement of a pendulum or the behavior of waves. They can also be used to model population growth, chemical reactions, and other phenomena.

5. How are 1st-order in time and 2nd-order in space differential equations solved?

There are various methods for solving these types of differential equations, including separation of variables, substitution, and using numerical methods. The specific method used will depend on the structure and complexity of the equation.

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