Solving Diff EQs: Find Solution & Related Functions

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more Diff EQ fun!

http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/58/6217226076d5fd259f53ad1e3ed4071.png
Find such a solution and then give the related functions requested.
http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/57/f15a6cea760ce4906a6ec16f9d29451.png
I submitted this:
http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/fb/2d83d3f390393ffc52b32ad0bd9fbf1.png
which was wrong! wee!

Here is my work:
http://img8.imageshack.us/img8/9514/lastscan6bj.jpg
 
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What's with the 1\sin (y) ? Are you sure it's not i\sin (y) ?
 
If it is indeed 1\sin (y) I get

F(x,y)=-7x^2-5x+e^y\left( 4\cos (y) + 5\sin (y)\right) =K

same as you.
 
yep that bad boy is definatley a 1, this program will randomly generate numbers, some people actually got 0's infront of theirs, i will e-mail the professor to see if the problem is working correctly!
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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