# Homework Help: Solving Simultaneous Equations

1. Jul 15, 2012

### Nano-Passion

I need help solving these two equations simultaneously

$y = c_1e^{r_1t_o}+c_2e^{r_2t_o}$

$y' = c_1r_1e^{r_1t_o}+c_2r_2e^{r_2t_o}$ My plan of solving these two equations is by substitution. By rearranging I obtain the following:

$c_1 = [y-c_2e^{r_2t_o}]e^{-r_1t_o}$
$c_1= \frac{[y' -c_2r_2e^{r_2t_o}]e^{-r_1t_o}}{r_1}$

Likewise,

$c_2=[y-C_1e^{r_1t_o}]e^{-r_2t_o}$
$c_2=\frac{[y'-c_1r_1e^{r_1e^r_1t_o}]e^{-r_2t_o}}{r_2}$

Don't know what to do from here.

Last edited: Jul 15, 2012
2. Jul 15, 2012

### Marioeden

Sorry, I don't see how these are two simultaneous equations. It's just the one equation you have for y and then you have its derivative with respect to t0 below it...

3. Jul 15, 2012

### Nano-Passion

No, I am are trying to simultaneously solve from equations y & y' for c_1 & c_2. [/I]

4. Jul 15, 2012

### Marioeden

ah right, you want c1 and c2 in terms of y and y'

So like multiply the first equation by r2 and subtract them, then you'll get c1. Do the same thing but multiply the first equation by r1 instead and subtract them and you'll get c2 :)

5. Jul 16, 2012

### Nano-Passion

Edit: Fixing Mistake

Okay so I get

$c_1 = \frac{[y'-yr_2]}{r_2-r_1}e^{-r_1t_o}$

The book gets the same answer but with r_1-r_2 in the denominator. Any ideas why? As long as I subtract the first equation from the second, I will always get r_2-r_1.

P.s. I'll solve the other half after I grab some food.

Last edited: Jul 16, 2012
6. Jul 16, 2012

### Marioeden

You may wanna double check your algebra, the book is right...