# Maximal interval of existence of the initial value problem

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Please solve the following initial value problem:

dx/dt = x^2 - 4, x(0) = 0.

and find the maximal interval of existence of the solution.

We solve the initial value problem using separation of variables. We use partial fractions to solve for the integral of 1/(x^2-4).

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##### Solution Summary

Given the first order differential equation, dx/dt = x^2 - 4, x(0) = 0, we solve it using separation of variables and find the maximal interval of existence of the solution.

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The differential equation is separable. We write

dx/dt = x^2 - 4

and follow the method for separable equations

dx/(x^2-4)=dt

Now integrate both sides (integral denoted as int)

int dx/(x^2-4)= int dt.

Now int dt=t+C, and int dx/(x^2-4) can be solved by partial ...

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