Second order DE

  • Thread starter EvLer
  • Start date
458
0
Hello, not sure if it's a typo in the book but I can't work this out:

y'' + y(x^2 + e^x) = 0;

It's second order but both dependent and independent variables are present, and i am stuck.
You don't have to solve it for me entirely, a hint would be great.

Thanks in advance.
 

dextercioby

Science Advisor
Homework Helper
Insights Author
12,950
532
The coeff are not constant and one is a polynomial and the other a transcendental function.I doubt one can find an analytical method to find the 2 solutions.

Daniel.
 
458
0
Are you saying that there's a typo in the problem?
(it's a first Diff Eq course)
 

HallsofIvy

Science Advisor
Homework Helper
41,712
876
Not necessarily. Many first course d.e. texts introduce "series solutions" but that's the only way I see to do this.
 

saltydog

Science Advisor
Homework Helper
1,582
2
When in doubt guess. I ain't proud. I used NDSolve with initial conditions (just out of thin air) of y(0)=1,y'(0)=0. The results are below. I know it's not a solution but at least it's the start of a handle. :smile:

Edit: Wait a minute. That IS a solution. I mean it's not an analytically derived one. :smile:
 

Attachments

Last edited:
458
0
HallsofIvy said:
Not necessarily. Many first course d.e. texts introduce "series solutions" but that's the only way I see to do this.
I'm sure it's somehow deducible with series, but unfortunately the book does not discuss that anywhere, i guess i'll have to google. I wish the book or the instructor would give more of "and why do we do this?" rather than "here's how: plug and chug".

Thanks everyone.
 
Last edited:
13
0
You should use series method to solve this diff eq.
It's hard to explain the method in this tiny box(!). I suggest to check out an elemantary diff eq book and read the chapter about the series method.
 

Related Threads for: Second order DE

  • Posted
Replies
5
Views
1K
  • Posted
Replies
3
Views
1K
Replies
2
Views
7K
Replies
5
Views
933
Replies
2
Views
19K
Replies
6
Views
799
Replies
4
Views
2K
Replies
4
Views
2K

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving

Hot Threads

Top