Should be a simple diff eq but my answer is different than the books

[myusernameis]

Homework Statement

dy/dt = 3+e^(-t) - 1/2*y

Homework Equations

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)

 

[D H]

Since you didn't show your work, it's a bit tough to know how you arrived at your answer. Show your work, please.

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.

 

[myusernameis]

Since you didn't show your work, it's a bit tough to know how you arrived at your answer. Show your work, please.

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.

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

 

[myusernameis]

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)..

 

[D H]

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

 

[myusernameis]

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

O LOLzzz

did i forget about c?

hahaha ...

 

[D H]

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.

 

[myusernameis]

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.

haha alright, thanks i think i got it