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**!!!For The Love of GOD!!! Diff Eq**

**1. Homework Statement**

I have done this problem 3 times. I am getting a sign error somewhere and I cannot find it.

When I solve this DE and then plug it back into the original, it is not checking out!!! Can anybody see my error? I would really appreciate a second set of eyes here. Clearly I am at that point where I just keep seeing what I think I am supposed to see!

Re writing the solution to the DE with the new constants is

[tex]x=-3/2\cos4t+3\sin4t+7/2\cos4t+1/2\sin4t=2\cos4t+19/4\sin4t[/tex]

[tex]y=3\cos4t-7/2\sin4t[/tex]

But when I differentiate and plug back into either if the originals, I am coming up with two sign errors...

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