Understanding Quick Differential Equation Concepts for Final Exam Preparation

[kguthrie]

Hey all, I hope this isn't against the forum rules or anything, but I'm studying for an upcoming final and had a quick question about one of the practice questions we have. I'm not sure I understand the concepts at work here, and was hoping someone could give me some insight.

http://img301.imageshack.us/img301/7656/40567729co1.png

Thanks in advance!

 

[Tac-Tics]

Hey all, I hope this isn't against the forum rules or anything, but I'm studying for an upcoming final and had a quick question about one of the practice questions we have. I'm not sure I understand the concepts at work here, and was hoping someone could give me some insight.

http://img301.imageshack.us/img301/7656/40567729co1.png

Thanks in advance!

Go through each answer and find the derivative. Then, check to see which satisfy the relationship in the question.

 

[HallsofIvy]

Another method, it this weren't "multiple guess", is to use "variation of parameters".

Knowing that $$\frac{2e^{2t}}{1+ e^{2t}}$$ is a solution, set
$$y= u(t)\frac{2e^{2t}}{1+ e^{2t}}$$
and substitute into the equation. That will give you a separable equation for u(t). Knowing that, you can find y.