• Support PF! Buy your school textbooks, materials and every day products Here!

Solve y'' = xy

  • #1
FeDeX_LaTeX
Gold Member
437
13

Homework Statement


Solve the differential equation y'' = xy


Homework Equations


-


The Attempt at a Solution


Not too sure what to do here. I looked it up and apparently the solution to this is the Airy function, but I don't understand how they got there. Help would be appreciated.
 

Answers and Replies

  • #2
33,084
4,791

Homework Statement


Solve the differential equation y'' = xy


Homework Equations


-


The Attempt at a Solution


Not too sure what to do here. I looked it up and apparently the solution to this is the Airy function, but I don't understand how they got there. Help would be appreciated.
What techniques do you know for solving differential equations? I have a particular method in mind, but there are possibly others.
 
  • #3
FeDeX_LaTeX
Gold Member
437
13
Separation of variables and solving 1st and 2nd order DEs with constant co-efficients -- not sure what to do here though since the co-efficient of y isn't a constant. I've heard that you solve this with a Taylor series expansion but I don't know how to apply that here. I've studied doing it by finding roots of the auxiliary equation and Taylor series, but I'm unsure of how to use the Taylor series method for this equation.
 
Last edited:
  • #4
FeDeX_LaTeX
Gold Member
437
13
You need boundary conditions to solve by method of Taylor series but I can't remember what they were. How would I approach this problem without knowing the boundary conditions (for the general case)?
 
  • #5
LCKurtz
Science Advisor
Homework Helper
Insights Author
Gold Member
9,508
730
You need boundary conditions to solve by method of Taylor series but I can't remember what they were. How would I approach this problem without knowing the boundary conditions (for the general case)?
You don't need boundary conditions. You will discover that you have no values for ##a_0## and ##a_1## and can get all the ##a##'s in terms of them. They will wind up being the two arbitrary constants.
 
  • #6
FeDeX_LaTeX
Gold Member
437
13
Never mind, solved it.
 

Related Threads for: Solve y'' = xy

  • Last Post
Replies
4
Views
811
Replies
5
Views
3K
  • Last Post
Replies
9
Views
1K
Replies
5
Views
7K
  • Last Post
Replies
2
Views
3K
Replies
4
Views
2K
  • Last Post
Replies
10
Views
1K
  • Last Post
Replies
5
Views
2K
Top