# Homework Help: Should be a simple diff eq but my answer is different than the books

1. Feb 10, 2009

1. The problem statement, all variables and given/known data
dy/dt = 3+e^(-t) - 1/2*y

2. Relevant equations

3. The attempt at a solution

how come i got y = 6e^(1/2t) + 2e^-t - 3

when the book has y = 6-2e^(-t) - 3e^(-t/2)

2. Feb 10, 2009

### D H

Staff Emeritus

It is rather easy to verify that your result is incorrect and that the book's is correct. Your result does not satisfy the given differential equation; the book's does. It is a good idea to always double check your work.

3. Feb 10, 2009

ok, it's just that it takes me a long time to type all the work, and i've done this problem for > 3 times now

ok, i'll type up my work haha

thanks

4. Feb 11, 2009

$1/2y + dy/dt = 3 + e^{-t}$

$e^{1t/2}y = 3 (integral)(e^{(1t/2)} + e^{-t}*e^{(1t/2)}$

$y = 6e^{(1t/2)}-2e^{(-1t/2)}$

that's only the general solution, since i need to get this right in order to figure out the particular solution...

it's actually (1/2)t, not 1/(2t)..

5. Feb 11, 2009

### D H

Staff Emeritus
Step 2 does not follow from step 3. You dropped a key factor.

6. Feb 11, 2009

O LOLzzz

hahaha .....

7. Feb 11, 2009

### D H

Staff Emeritus
No, you did not forget about c. (Well, you did, but that is not what I was talking about.)

Look at the left-hand side of your second equation.

8. Feb 11, 2009