# Simple First Order ODE

1. Nov 28, 2008

### leopard

y'(t) - ay(t) = 0

What is the form of the solution? $$C \cdot e^{at}$$

?

I have this ODE:

$$T'(t) - (1 - \frac{n^2}{4})T(t) = 0$$

If I'm right, the solutions should be of the form

$$C \cdot e^{(1- \frac{n^2}{4})t}$$

My book, however, says

$$C \cdot e^ {1- \frac{n^2}{4}t}$$

Who's right?

Last edited: Nov 28, 2008
2. Nov 28, 2008

### Office_Shredder

Staff Emeritus
I think the book forgot some parentheses

3. Nov 28, 2008

### leopard

Brilliant.

y' = (y - x)^2

what's the form of the solution here?

I find it hard to determine the form of solution of differential equations.

Last edited: Nov 28, 2008
4. Nov 28, 2008

### Dick

I would try a simple substitution first. How about v=y-x? Now see if you can separate it in those variables.