# How do you solve #x''(t)+x3=0#?

General solution:

where

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To solve the differential equation x''(t) + x^3 = 0, we can use a method called the shooting method or numerical methods because this is a nonlinear differential equation and does not have a general analytical solution.

In the shooting method, we convert the second-order differential equation into a system of first-order differential equations by introducing a new variable. This allows us to apply numerical techniques like Euler's method, the Runge-Kutta method, or other numerical methods to approximate the solution.

Alternatively, software packages like MATLAB or Python libraries such as SciPy can be used to solve this differential equation numerically.

However, if you're interested in an analytical approach, it might not be possible for this specific equation due to its nonlinear nature.

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