Non-linear 2rd diff. eqtn.

1. Jun 29, 2011

athrun200

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

I just want to ask how to obtain the solution?
What mathematical method involved?

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2. Jun 29, 2011

ehild

Replace back the given function into the differential equation and see if it is really the solution.

ehild

3. Jun 29, 2011

What makes you think this is Non Linear?

4. Jun 29, 2011

athrun200

I just want to know, if I only have the first line, how can I get second line?
Just by try and error?

5. Jun 29, 2011

athrun200

I see there is a square there.:tongue:

6. Jun 29, 2011

ehild

Is the second line solution of the differential equation?

ehild

7. Jun 29, 2011

ideasrule

It's still linear because neither psi nor the second derivative of psi is being squared. However, the second line isn't the solution, and there's no solution in terms of elementary functions:

http://www.wolframalpha.com/input/?i=y%27%27%3Dx^2*y

8. Jun 29, 2011

athrun200

I saw the eqtn from this book.
Does it mean that the approximation is wrong?

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9. Jun 30, 2011

ehild

If you calculate the second derivative of Ψ=exp(±z2/2) you will find that it is (z2±1)Ψ. Therefore the Ψ-s are only approximate solution, valid for z2>>1.

ehild