Given the initial value problem equation h' -kh'/2, h(0) = 25, where k > 0. Mark the appropriate box. This equation is linear nonlinear What can you conclude about existence and uniqueness of the solution based on the theorems stated in class? Mark all that apply A continuous solution y(t) exists everywhere A continuous solution y(t) exists for some undetermined open interval containing t = A continuous solution y(t) exists for some undetermined open interval containing t 25 Many solutions can exist since the righthand side is not differentiable everywhere. A unique continuous solution is guaranteed to exist locally. Find the solution to the initial value problem.

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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.