# How can I find the analytical solution for the system?

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## Homework Statement

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

Omega,N0 and k are positive .

## The Attempt at a Solution

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

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LCKurtz
Homework Helper
Gold Member
Show us what happens with the Bernoulli substitution so we can see what your difficulty is.

Mark44
Mentor
Here's the DE in a bit more readable form.
$$\frac{dx}{dt} = N_0x(\sin(\omega t) - \frac{x}{k})$$

Last edited:
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.

LCKurtz