Non-linear 2rd diff. eqtn.

[athrun200]

Homework Statement

Homework Equations

The Attempt at a Solution

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

 

[ehild]

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

ehild

 

[Saladsamurai]

What makes you think this is Non Linear?

 

[athrun200]

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

ehild

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

 

[athrun200]

What makes you think this is Non Linear?

I see there is a square there.:tongue:

 

[ehild]

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

Is the second line solution of the differential equation?

ehild

 

[ideasrule]

I see there is a square there.:tongue:

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

 

[athrun200]

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

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

 

[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