How Do You Determine p(x) and q(x) in a Second Order ODE with Given Solutions?

[brad sue]

Hi ,
please can I have your help?

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.

 

[StatusX]

Try again. Write out the two equations you get and solve for p and q as if they were variables and x was a constant. The two equations will be identical except for the factor in front of q (ie, y), since the two solutions only differ in their constant term (so that all their derivatives will be equal).