Wright M

This is a fairly easy one, I just want to make sure I'm right. (Practice test with no answers)

Determine all values of r for which the equation y'+2y=0 has solutions of the form y = e^rt

My work:

y' + 2y = 0

y = e^rt

y' = re^rt

so

re^rt + 2e^rt = 0

r = -2

That's the only r-value I could find. Thanks!

I have a problem that my teacher gave for a practice test (no answers), but it is unlike anything I can find in my book or online.

Find the general solution of ty' - y = (y^2)(e^ -t)

For every problem I've seen like this you need the equation to be of a specific form to find an integrating factor (y' - ay = f(t)). I've never seen a problem like this with a y^2 on the RHS, and I don't know what to do. Please help!

The Bible says we are "made in God's image." Why would God have even a vague resemblance to us? Since he was around before the existence of light, why would he need eyes? Since he was around before the existence of sound, why would he need ears? Every part of the human body exists for a reason given our surroundings, needs, things available to us, etc.

Just something I've been thinking about.

The more details, the better!

Note:

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I wouldn't have a ticket.

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