# Second order DE

#### EvLer

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.

Related Differential Equations News on Phys.org

#### dextercioby

Homework Helper
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.

#### EvLer

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

#### HallsofIvy

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

#### saltydog

Homework Helper
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.

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

#### Attachments

• 6.1 KB Views: 264
Last edited:

#### EvLer

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:

#### pmrazavi

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.

### 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