Partial Differential Equation? What is this?

In summary, the conversation is about a difficult homework problem that requires solving a differential equation using a specific form of solution. The person is struggling to understand how to start and is asking for clarification on how to substitute the given equation into the differential equation.
  • #1
JefeNorte
9
0
The professor passed this out today for homework and I have no idea how to even get started. If someone could tell me what type of problem this is I could look it up in the textbook but I can't find anything similar. I couldn't figure out how to insert all of the symbols so I attached the problem as a .gif
 

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  • #2
What exactly is your problem? The paper leads you step by step through the solution. It says

"Seeking a solution of the form u= f(x) cos([itex]\omega[/itex]t)+ g(x) sin([itex]\omega[/itex]t), show that ..."

Okay, put that into the differential equation and see what must be true of f and g in order to satisfy the equation.
 
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  • #3
I have been trying to figure out this problem for a week now and I am still drawing a blank on how to "put that into the differential equation." How exactly can I get started on this?
 
  • #4
Do you know how to "substitute" into an equation? The problem is askng you to substitute u= f(x) cos(t)+ g(x) sin(t) into the equation and tell what must be true of f and g in order to satisfy the equation.
 
  • #5
I'm not sure I understand exactly what you are talking about. What am I substituting u= f(x) cos(t)+ g(x) sin(t) into? The du/dt=D*(d2u/dx2) equation?
 
  • #6
Yes! That's the only equation you are given at that point!
 

What is a partial differential equation?

A partial differential equation (PDE) is a mathematical equation that involves multiple independent variables and their partial derivatives. It is used to describe how a quantity, such as temperature or pressure, changes over time and space.

What are some real-world applications of partial differential equations?

Partial differential equations are used in many fields, including physics, engineering, economics, and biology. They can be used to model and predict a wide range of phenomena, such as heat transfer, fluid dynamics, and population growth.

How are partial differential equations solved?

Solving a partial differential equation involves finding a mathematical function or set of functions that satisfy the equation. This can be done analytically, using techniques such as separation of variables or the method of characteristics, or numerically, using computational methods.

What is the difference between an ordinary differential equation and a partial differential equation?

An ordinary differential equation (ODE) involves only one independent variable, while a partial differential equation involves multiple independent variables. This means that the solutions to ODEs are functions of a single variable, while the solutions to PDEs are functions of multiple variables.

Why are partial differential equations important in science?

Partial differential equations are important in science because they provide a powerful mathematical tool for describing and predicting complex phenomena in a wide range of fields. They allow scientists to model and understand the behavior of systems that would be difficult or impossible to study using traditional methods.

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