Is this differential equation separable?

-EquinoX-
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Yes, it is separable. Use the laws of logarithms. ln(s^(5t))=(5t)*ln(s). Now separate it.
 
how do you go on separating it after that? my guess would be:

the 8t^4 confuses me
 
What do you get after you apply the log law? Factor out the t^4. The question is just asking whether it's separable.
 
t^3*(5t)*ln(s) + 8t^4
 
-EquinoX- said:
t^3*(5t)*ln(s) + 8t^4

Well? Keep going. t^3*5*t=5t^4...
 

Thread 'Finding the nth roots of a complex number'

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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