The given initial value problem is:
If p(x), q(x) and g(x) are continuous on the interval [a,b], then the second order differential equation
has a unique solution defined for all x in [a,b].
Redefine the differential equation as follows.
Compare the above equation with standard equation of initial value problem.
Then, and and
The function p(t) is continuous for all values of t except t=w and t=-2
The function q(t) is continuous for all values of t except t=w and t=-2
The domain of the both the function is
Thus, the function has a unique solution at the point t=1 on the largest interval (-2,2)
Answer:
The solution to the initial value problem exist on the largest interval is (−2, 2).
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