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

  • Thread starter brad sue
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In summary, In order to find the ODE with fundamental solutions of x^2+2 and x^2-2, first write out the equation y''+p(x)y'+q(x)y=0 and then substitute the two solutions into it. Since the two solutions have identical derivatives, the equations for p(x) and q(x) will be identical except for a factor in front of q. Solve for p(x) and q(x) as if they were variables with x as a constant to find the ODE.
  • #1
brad sue
281
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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.
 
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  • #2
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).
 

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

What is p(x) and q(x)?

p(x) and q(x) are mathematical representations of a polynomial equation. They are used to represent the coefficients and variables in a polynomial function.

How do I find p(x) and q(x)?

To find p(x) and q(x), you will need to have a polynomial equation in the form of ax^2 + bx + c. Then, p(x) will be equal to a and q(x) will be equal to b + c.

Why is it important to find p(x) and q(x)?

Finding p(x) and q(x) is important because it allows us to graph the polynomial function and determine important characteristics such as the x-intercepts, y-intercept, and end behavior.

What are some tips for finding p(x) and q(x)?

One tip for finding p(x) and q(x) is to first identify the coefficients of the polynomial equation. Then, use the formula p(x) = a and q(x) = b + c to find the values of p(x) and q(x).

Can I use a calculator to find p(x) and q(x)?

Yes, you can use a calculator to find p(x) and q(x). However, it is important to understand the concept and be able to find them manually as well.

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