# Homework Help: Seemingly Non-Separable Differential Equation

1. Nov 1, 2012

### danomite

1. The problem statement, all variables and given/known data

I am trying to find the parametric equation that describes the following second order differential equation:

2. Relevant equations

$m\frac{d^2y}{dt^2}=-mg - k\frac{dy}{dt}$

Where m, g, and k are all constants.

3. The attempt at a solution

I substituted $u=\frac{dy}{dt}$ to reduce the order of the equation to one. Now I have:

$m\frac{du}{dt}=-mg-ku$

And I have been stuck here. I don't see how to separate the variables, can anybody help out?

2. Nov 1, 2012

### micromass

It's just a linear differential equation with constant coefficients. Have you seen how to solve these??

3. Nov 1, 2012

### danomite

I have seen how to solve simple ones. My main problem here is isolating t and u. The algebra doesn't work out, and I've been so far unsuccessful in finding a substitution that will separate these variables.

4. Nov 1, 2012

### arildno

Find a suitable CONSTANT addition to "u"

5. Nov 1, 2012

### HallsofIvy

Since there is no variable, t, itself in the equation, it is pretty trivial to separate!

$m\frac{du}{ku+ mg}= - dt$

Now integrate both sides.