Any analytical solutions to this second order nonlinear DE?

  • Thread starter pivoxa15
  • Start date
  • #1
2,259
1
Are there any analytical solutions to:

ay''+bx^2y+cxy+dy=0

where a,b,c,d are constants and y(x)

If so how would you go about it? Is there a website that teaches you how to solve these?
 

Answers and Replies

  • #2
HallsofIvy
Science Advisor
Homework Helper
41,847
966
If by "analytical solutions" you mean "closed form solutions" then, in general no. The standard method of solution for such a function is to use an infinite series.
 
  • #3
arildno
Science Advisor
Homework Helper
Gold Member
Dearly Missed
10,025
134
What you've written is a LINEAR ODE, BTW.
 
  • #4
mathwonk
Science Advisor
Homework Helper
2020 Award
11,267
1,470
the usual technical meaning of the word "analytic" is a function defined by a power series, and in that sense , as Halls implied, the answer is yes.
 

Related Threads on Any analytical solutions to this second order nonlinear DE?

Replies
2
Views
7K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
3
Views
4K
  • Last Post
Replies
0
Views
2K
  • Last Post
Replies
22
Views
5K
  • Last Post
Replies
6
Views
3K
Replies
1
Views
5K
Replies
1
Views
2K
Replies
2
Views
2K
Top