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

In summary, the student attempted to solve for y using the differential equation and dropped a key factor. The student was not able to solve for y and needed to look at the left-hand side of the equation.
  • #1
myusernameis
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0

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)
 
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  • #2
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.
 
  • #3
D H said:
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
 
  • #4
[itex]1/2y + dy/dt = 3 + e^{-t}[/itex]

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

[itex]y = 6e^{(1t/2)}-2e^{(-1t/2)}[/itex]

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
Step 2 does not follow from step 3. You dropped a key factor.
 
  • #6
D H said:
Step 2 does not follow from step 3. You dropped a key factor.

O LOLzzz

did i forget about c?

hahaha ...
 
  • #7
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
D H said:
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
 

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

1. Why is my answer different from the one in the book?

There could be several reasons for this. It is possible that there is a mistake in your calculations or you have made an error in solving the differential equation. It is also possible that the book has a different version of the problem or uses a different method to solve it. Double-check your work and try to understand the steps the book took to solve the problem.

2. Is my solution still correct even though it is different from the book?

If you have followed the correct steps and your solution satisfies the given differential equation, then your solution is correct. Keep in mind that there are often multiple ways to solve a differential equation, so your solution may differ from the one in the book but still be valid. However, if you are unsure, you can always ask a teacher or consult other resources for confirmation.

3. Should I always expect my solution to match the one in the book?

No, not necessarily. As mentioned before, there can be different methods and approaches to solving a differential equation. Additionally, there may be typos or errors in the book. It is more important to understand the steps and concepts behind solving the problem rather than getting the exact same answer as the book.

4. What should I do if I am stuck and cannot solve the differential equation?

If you are struggling to solve the differential equation, it is always helpful to review the fundamental concepts and techniques of differential equations. You can also seek help from a teacher or tutor, or consult other resources such as textbooks, online tutorials, or practice problems. It may also be helpful to break the problem down into smaller parts and tackle them one at a time.

5. Is it possible to get the same answer as the book but using a different method?

Yes, it is possible. As long as your solution satisfies the given differential equation and you have followed the correct steps, your method may differ from the one in the book but still yield the same answer. However, it is always beneficial to understand and practice different methods to solve differential equations as it can help improve your problem-solving skills.

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