Solving Integral Equation: x(t) = -8?

brusier
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Homework Statement



I integrated dx/dt = x^2+(1/81)

Homework Equations



My result; 9(arctan(9x))= t+C needed to be solved for initial condition x(0)=-8
and fit into x(t) = format

The Attempt at a Solution



I cannot figure out why the computer is not accepting my solution:
arctan (9x)= (t-14.012)/9
 
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Wouldn't that be:

x(t)=\frac{(tan(\frac{t-14.012}{9}))}{9}
 
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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