Solve the Separable Differential Equation for u

jwj11
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Homework Statement



Solve the separable differential equation for u

du/dt = e^(6u + 8t)

Use the following initial condition: u(0) = 13.

Homework Equations



Techniques for solving separable differential equations.

1. Group variable and respective dy,dx,dz, etc. together
2. Integrate both sides
3. Solve for C using given data point
4. Solve for dependent variable

The Attempt at a Solution



http://img177.imageshack.us/img177/7321/differentialequation.jp
 
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It isn't incorrect. What makes you think otherwise?
 
Hmm.. I guess I am inputting it wrong. This is part of a webwork assignment (an online submission assignment)
 
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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