# help with ODE

Joined Dec 29, 2004
83
Sorry I made a mistake about the forum. I tried to delete it but I dont see where to do it pleas redirect this post in homework help/math
Hi ,

x^2+2 and x^2-2 are fundamental set of solutions of a second order ODE. find the ODE.
form:y''+p(x) y'+ q(x) y=0.

I tried to replace the two solutions in the equation but because those solutions have exact same first and second derivatives, I found p(x)=q(x)=0 !!!!

Can you help me to find p(x) and q(x)?
Thank you
B.

#### Papabravo

Joined Feb 24, 2006
16,180
Originally posted by braddy@May 8 2006, 10:26 PM
Sorry I made a mistake about the forum. I tried to delete it but I dont see where to do it pleas redirect this post in homework help/math
Hi ,

x^2+2 and x^2-2 are fundamental set of solutions of a second order ODE. find the ODE.
form:y''+p(x) y'+ q(x) y=0.

I tried to replace the two solutions in the equation but because those solutions have exact same first and second derivatives, I found p(x)=q(x)=0 !!!!

Can you help me to find p(x) and q(x)?
Thank you
B.
[post=16934]Quoted post[/post]​
Polynomials are not generally the solutions of ODEs. Generally exponetial functions are required. I'm not familiar with the specific terminology "fundamental set of solutions". I'm familiar with a general solution involving two arbitrary constants in the case of a second order equation and I'm familiar with the particular solution based on the initial conditions. Can you be more precise about the notion of fundamental set of solutions?

Here is my next problem. If y is a function of x, then the expression above is not a differential equation at all but a simple product of polynomials, which should have an algebraic solution. This solution may not be unique since p(x) and q(x) do not appear to be constrained.