Check that for all t0 a the existence and uniqueness theorem

Check that for all t_0, a the existence and uniqueness theorem applies to the ivp In x\' = x^2, x(t_0) = a.

ln x\' = x²

Taking derivative

f(x,y) = 2x

x = a

y = 2a

Hence , both functions are defined and continuous in a region around (a, a), this IVP satisfies the hypotheses of Theorem 1,

$Check that for all t_0, a the existence and uniqueness theorem applies to the ivp In x\' = x^2, x(t_0) = a.Solutionln x\' = x2 Taking derivative f(x,y) = 2x x$

Check that for all t0 a the existence and uniqueness theorem

Solution

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