Solving a Second Order Differential Equation: Help Needed

[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.

Thanks in advance.

 

[dextercioby]

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]

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

 

[saltydog]

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.

 

[EvLer]

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.

 

[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.