# Differential Equation

1. Feb 6, 2010

### Nusc

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

$$\frac{dx}{dt} =\frac{ -x}{(t-1+e^{-x})}$$

Show that an approximate solution leads to,

$$\frac{dx}{dt} = -\frac{ 1}{1-c1} [c1+(c2 + \frac{c2-c1/2}{1-c1})*t + O(t^3)]$$

2. Relevant equations

3. The attempt at a solution

The first equation is not separable.

To approximate, assume
$$x = c1*t+c2*t^2 + O(t^3)$$
Hence
$$dx/dt = c1 + 2*c2*t + O(t^2).$$

If I equate

$$dx/dt = c1 + 2*c2*t + O(t^2).$$

and

$$\frac{dx}{dt} =\frac{ -x}{(t-1+e^{-x})}$$

Should I immediately taylor expand the exponential?

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?