I am solving a nonlinear ODE in the form of Newton's Second Law. In the equation, there is a Heaviside Theta Function of the function which I am solving (##\theta (x(t)##). Since it is quite troublesome to have both the left side of the ODE and the imput of the ODE to contain function of unknown function, I am considering using a transformation which can be nonlinear because linear transformation cannot help me separate the composition of two functions. Is there an analytical way to solve the equation?(adsbygoogle = window.adsbygoogle || []).push({});

P.S. Here is my equation

[tex]x''(t)+\omega_0^2 x(t)=[\vartheta(x(t)+b) \cdot \vartheta(x(t)-b)] \cdot \sin(\omega t)[/tex] where ##\omega## and ##\omega_0## are independent.

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# Nonlinear transform can separate function composition?

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