Solving 2nd ODE and Multivariable Calculus for Wave Equation

• weakness66
In summary: It appears to be some sort of "boundary condition" problem. I think the OP has to fill in the blank spaces with the proper functions. In summary, the conversation involves a request for help with a coursework on 2nd ODE and multivariable calculus. The situation presented includes the one-dimensional wave equation and values for a string stretched between x=0 and L=2, with fixed ends and a raised distance at x=b and released from rest at t=0. The conversation also discusses the initial position and possible homework implications.
weakness66
Hello guys,
I would like to ask some questions regarding my coursework, which is about 2nd ODE and multivariable calculus.
Since we have the one-dimensional wave equation and values for the string stretched between x=0 and L=2: 0≤x≤L, t≥0
The string is fixed at both ends so we have :
u(_,t)=u(_,t) = 0 , t≥0
now we assume string is raised a distance μ at x=b and released from rest at t=0, Zero velocity implies: ∂u/∂t (_,_)=0 . 0≤x≤L

thanks beforehand!

Welcome to PF;
I would like to ask some questions regarding my coursework...
That's what we are here for. However, you didn't ask any questions. Instead, you appear to have presented a situation.

Since we have the one-dimensional wave equation and values for the string stretched between x=0 and L=2: 0≤x≤L, t≥0
The string is fixed at both ends so we have :
u(_,t)=u(_,t) = 0 , t≥0
now we assume string is raised a distance μ at x=b and released from rest at t=0, Zero velocity implies: ∂u/∂t (_,_)=0 . 0≤x≤L
... what are the underscore characters supposed to represent in the above?

Are these blanks in the question you are supplied with?

weakness66 said:
Hello guys,
I would like to ask some questions regarding my coursework, which is about 2nd ODE and multivariable calculus.
Since we have the one-dimensional wave equation and values for the string stretched between x=0 and L=2: 0≤x≤L, t≥0
The string is fixed at both ends so we have :
u(0,t)=u(2,t) = 0 , t≥0
now we assume string is raised a distance μ at x=b and released from rest at t=0, Zero velocity implies: ∂u/∂t (x,0)=0 . 0≤x≤L

thanks beforehand!

And the initial position is u(x,0) = ? Or is that what you are asking?

I'm concerned that this is a homework question of the "fill in the blanks" style.
If that is the case then LCKurtz may just have done your homework for you - well done!
You should be able to figure the initial function though.

Simon Bridge said:
I'm concerned that this is a homework question of the "fill in the blanks" style...

Perhaps you are correct, although I wouldn't expect something that trivial here.

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 commonly used to describe physical phenomena that involve acceleration, such as the motion of a mass on a spring or the behavior of a vibrating string.

2. How is the wave equation related to second-order differential equations?

The wave equation is a specific type of second-order differential equation that describes the propagation of a wave through a medium. It is commonly used in physics and engineering to model various wave phenomena, such as sound waves, electromagnetic waves, and water waves.

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

To solve a second-order differential equation, you need to find a function that satisfies the equation. This can be done using various techniques, such as separation of variables, substitution, or using an integrating factor. The specific method used will depend on the structure and complexity of the equation.

4. What is multivariable calculus?

Multivariable calculus is a branch of mathematics that deals with functions of multiple variables. It extends the concepts of single-variable calculus to functions with two or more independent variables, and is used to solve problems in fields such as physics, engineering, and economics.

5. How is multivariable calculus applied to the wave equation?

In the context of the wave equation, multivariable calculus is used to study the behavior of waves in multiple dimensions. This includes analyzing the direction and rate of change of waves, determining the maximum and minimum values of a wave function, and finding the equation of a wave's path in a given medium. Multivariable calculus is also essential for understanding the boundary conditions and solutions to the wave equation in different physical scenarios.

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