Consider the following initial value problem: = sin(y +t) +e - sin(e' +t), y(0) = 2 Show that there exists an interval ICR such that 0 e I, and a differentiable function y:IR which is a solution to this initial value problem. Is the solution in (a) unique? Explain why or why not. One of the following three things is true: 1. y(t) >e for all tel 2. y(t)

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.