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. (10 points) Determine whether or not the fundamental existence and uniqueness theorem guarantees a unique solution to the following initial value problem. Show your work, clearly indicating any conditions

which must be checked as well as your final conclusion. \begin{array}{c} \frac{d y}{d x}=\frac{2(y-1)^{1 / 5}}{\sqrt{x+3}}+3 y^{4} \\ y(3)=1 \end{array} What is the set of all initial conditions (xo, Yo) through which \frac{d y}{d x}=\frac{2(y-1)^{1 / 5}}{\sqrt{x+3}}+3 y^{4} \text { is guaranteed to have a unique solution? }

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