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.© BrainMass Inc. brainmass.com September 23, 2018, 1:55 pm ad1c9bdddf - https://brainmass.com/math/integrals/maximal-interval-existence-initial-value-problem-515449
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The differential equation is separable. We write
dx/dt = x^2 - 4
and follow the method for separable equations
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 ...
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.