How can I solve this 2nd degree differential equation?

[Kosta1234]

Homework Statement

Hello.
I'm trying to do some problem and I can't solve some differential equation from the 2nd degree:

X'' - (F₀ / ( d * m)) * X = 0

d, m, F are constant that are known

Homework Equations

I know that solution is a trigonometry equation. But I want to see how to solve this..

The Attempt at a Solution

Thanks.

 

[haruspex]

solution is a trigonometry equation

Not with that minus sign.*
One way to solve this is to multiply through by X'. Can you see how to proceed from there?

*Edit: unless you meant hyper trig.

 

[DrClaude]

The Attempt at a Solution

You have to provide an attempt at a solution. Please show what you have tried so far.