Solution of the differential equation $ddotx(t)+sin(omega t)x(t)=cos[eta(t)]$
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The differential equation:
$$ddotx(t)+sin(omega t)x(t)=cos(eta t)$$
has an analytical solution involving Mathieu functions.
This is valid if both $omega$ and $eta$ are constant.
Suppose the term $eta$ is a normal distribuited random variable $eta(t)$ with mean $mu$ equal to zero and variance $sigma^2$. How changes the solution?
Or better: Is it possible to find analytically the spectrum of $x(t)$? Thanks
differential-equations stochastic-processes special-functions stochastic-calculus
add a comment |Â
up vote
1
down vote
favorite
The differential equation:
$$ddotx(t)+sin(omega t)x(t)=cos(eta t)$$
has an analytical solution involving Mathieu functions.
This is valid if both $omega$ and $eta$ are constant.
Suppose the term $eta$ is a normal distribuited random variable $eta(t)$ with mean $mu$ equal to zero and variance $sigma^2$. How changes the solution?
Or better: Is it possible to find analytically the spectrum of $x(t)$? Thanks
differential-equations stochastic-processes special-functions stochastic-calculus
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
The differential equation:
$$ddotx(t)+sin(omega t)x(t)=cos(eta t)$$
has an analytical solution involving Mathieu functions.
This is valid if both $omega$ and $eta$ are constant.
Suppose the term $eta$ is a normal distribuited random variable $eta(t)$ with mean $mu$ equal to zero and variance $sigma^2$. How changes the solution?
Or better: Is it possible to find analytically the spectrum of $x(t)$? Thanks
differential-equations stochastic-processes special-functions stochastic-calculus
The differential equation:
$$ddotx(t)+sin(omega t)x(t)=cos(eta t)$$
has an analytical solution involving Mathieu functions.
This is valid if both $omega$ and $eta$ are constant.
Suppose the term $eta$ is a normal distribuited random variable $eta(t)$ with mean $mu$ equal to zero and variance $sigma^2$. How changes the solution?
Or better: Is it possible to find analytically the spectrum of $x(t)$? Thanks
differential-equations stochastic-processes special-functions stochastic-calculus
differential-equations stochastic-processes special-functions stochastic-calculus
asked Sep 5 at 8:39
Riccardo.Alestra
6,00811951
6,00811951
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