The discussion revolves around a first-order differential equation given by dy/dt = 3 + e^(-t) - 1/2*y. The original poster expresses confusion regarding their solution compared to the solution provided in a textbook.
Some participants have pointed out potential errors in the original poster's calculations and have encouraged them to show their work for better clarity. There is an ongoing examination of the steps involved in solving the differential equation, with hints at missing factors and the importance of constants in the solution.
The original poster mentions having worked on the problem multiple times, indicating a struggle with the solution process. There is also a note about the difficulty in typing out the work, which may affect the clarity of the discussion.
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.
D H said:Step 2 does not follow from step 3. You dropped a key factor.
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.