# Eliminating constants

1. Oct 17, 2012

### th3chemist

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

eliminating c1 and c2 from y, y' and y'' to create a differential equation

2. Relevant equations

I have the equation y = (c1 +c2x)e^x
y' = c2e^x +(c1+c2x)e^x
y'' = c2e^x + c2e^x + (c1+c2x)e^x)

(from product rule)

3. The attempt at a solution

I'm just not sure how to eliminate the constants. If I try to do y'' - y i still have constants left.

2. Oct 17, 2012

### SammyS

Staff Emeritus
What do you get if you plug y = (c1 +c2x)ex for the second term in y' ?

Solve that for c2.

3. Oct 17, 2012

### bigfooted

with y"-y you are only using part of you available information.
What happens if you subtract y-y' = ... ?
or y'-y" ?

4. Oct 17, 2012

### th3chemist

thank you! I can't believe I didn't see that.

I got c2 = (y' - y)/ e^x. I can then sub this into y'' to get the differential.

Thank you :)

Last edited: Oct 17, 2012
5. Oct 17, 2012

### lendav_rott

Isn't it c2 = (y' - y) e^-x ?

6. Oct 17, 2012

### th3chemist

yes yes, for some reason it didn't put the / button