Help with Laplace Transforms of Autonomous & Delayed Functions

thang
Messages
1
Reaction score
0
Could you please help me to do Laplace transformation ? That is an autonomous and nonlinear function on the right-hand side

L{dx/dt}=L{1/1+x^a}

where a is an integer

other kind is in the form of delay

L{dx/dt}=L{sin(x(t-\tau))}

where \tau is delay, and real number
 
Physics news on Phys.org
What have you done so far? Where do you get stuck?
 
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...
Back
Top