y(x) = C,e*+C,e*cosx is a solution to the equation y"-3y"+4y'-2y 0 for any pair of constants (C, ,C) 2) Show that there is no pair of constants (C, ,C,) for which y(x) above satisfies the following IC's y(0) = 1, y'(0) = 0, y"(0) = 0

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A: Since you have posted multiple question, I can do first question as per our company guidelines.…

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A: follow next step

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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.