How can I find the analytical solution for the system?

  • Thread starter Avan
  • Start date
  • #1
25
0
Member warned about posting with no effort shown

Homework Statement



dx(t)/dt = N0*sin(omega*t) * x(t) - ( N0*x^2 / k )

Omega,N0 and k are positive .

Homework Equations




The Attempt at a Solution


I tried to solve it using the Bernoulli equations but I could not get the last result.
 

Answers and Replies

  • #2
LCKurtz
Science Advisor
Homework Helper
Insights Author
Gold Member
9,557
767
Show us what happens with the Bernoulli substitution so we can see what your difficulty is.
 
  • #3
34,688
6,394
Here's the DE in a bit more readable form.
$$ \frac{dx}{dt} = N_0x(\sin(\omega t) - \frac{x}{k})$$
 
Last edited:
  • #4
25
0
The result that I got is :

exp( (cos(omega*t) * (-N0/omega)) / x(t) = (N0 / k) * ( integral (exp( (cos(omega*t)) * (-N0/omega) ) ) ) dt

So I do not know how to find the integral when typically there is no specific solution for the integral of the Exponential function.
 
  • #5
LCKurtz
Science Advisor
Homework Helper
Insights Author
Gold Member
9,557
767
You may just have to express the result in terms of unevaluated integrals. Integrals of the form ##\int e^{\frac 1 \omega \cos(\omega t)}~dt## don't have elementary antiderivatives.
 

Related Threads on How can I find the analytical solution for the system?

Replies
5
Views
632
  • Last Post
Replies
0
Views
2K
  • Last Post
Replies
7
Views
2K
Replies
6
Views
3K
Replies
4
Views
1K
Replies
1
Views
650
  • Last Post
Replies
1
Views
2K
Replies
13
Views
2K
Replies
11
Views
3K
Replies
5
Views
2K
Top