Thread: Puzzles with some PDE

Hello, folk!!

I'm studying something on professor's notes...

Could anybody suggest me where I can find something on line to verify solutions of equations in (3.94) and (3.95) (look at http://img46.imageshack.us/my.php?im...ndito01gp2.jpg ) are functions in (3.96) for ni different from zero and (3.97) ( http://img80.imageshack.us/my.php?im...ndito02xy1.jpg ) for ni =0?

Moreover, why does text tell me ni must be an integer and p_0 =0 in order that solution is "with unique value"?

Thanks!

They are ODE, not PDE. (3.94 is the equation of simple harmonic motion.)

To verify whether an equation is a solution of an ODE, you can just differentiate and substitute into the ODE. That’s all there is to it. Solving a differential equation is one thing, but checking whether a given equation is a solution is another.

Anyway, this site is very handy for differential equations of all sorts: http://eqworld.ipmnet.ru/

I'm desolated for the PDE mistake (it is because equations in 3.94 and 3.95 have been obtained starting from a PDE..so I get confused)...


Could anybody help me about the question on ni integer and p_0 =0?