Partial Differential Equation? What is this?

[JefeNorte]

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

 

[HallsofIvy]

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($\omega$t)+ g(x) sin($\omega$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.

 

[JefeNorte]

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?

 

[HallsofIvy]

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.

 

[JefeNorte]

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?

 

[HallsofIvy]

Yes! That's the only equation you are given at that point!