What is the Solution to a Simple Differential Equation with Constant Parameters?

[Wildcat04]

Homework Statement

I need to integrate this problem, I am not sure what it is but I am having trouble doing this simple problem and coming up with the right answer. Its been awhile since I had diff eq..

Solve for w as a function of x

0 = g + \upsilon (d²w / dx²)

g, \upsilon = constant

Homework Equations

Problem Solution:

w = (g/\upsilon)(bx - x²/2)

The Attempt at a Solution

I am assuming that I need to move stuff to each side and complete the double integrals and solve for w

something along these lines:

-g dx² = \nu d²w

I would love it if someone could give me a nudge.

 

[Dick]

It's really easy. You've got w''(x)=(-g/v). Just integrate both sides with respect to x twice. Don't forget the constants of integration. You should then realize the problem solution isn't the most general one.

 

[Wildcat04]

Thank you Dick, I knew that I was making this stupid problem much harder then it should be put I just couldn't wrap my head around it.