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y' = f(y, t), y(t0) = y0. (i) what conditions guaranteeing a unique solution to the...

y' = f(y, t), y(t0) = y0.

(i) what conditions guaranteeing a unique solution to the nonlinear initial value problem

(ii) After checking the conditions,  state what the theorem predicts for the initial value problem y' = (-x2 )/y , y(1) = 0.

(iii) Solve the above initial value problem and find two distinct solutions

(iv) Explain if results in (iii) and in (ii) contradict each other

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