Ordinary differential equation question

[real analyst]

Homework Statement

What is the general solution to the following ODE

F=X''m where F and m are both constants

Homework Equations

The Attempt at a Solution

I got X=(k/2)t^2 + C

I got this from F/M being just another constant K, and X'' being (d^2 X)/(dt^2) so you just integrate k twice with respect to t, the first giving kt, and the second giving (k/2)t^2 + C. Is this correct?

 

[ircdan]

almost but not quite,

assuming m != 0, F = X''m => F/m = X'' , so X' = (F/m)x + C, say k = F/m, so

X' = kx + C, now integrate again,

X = kx^2/2 + Cx + D

 

[real analyst]

yep, stupid mistake. thanks a lot!