3. For any real number a, verify that the functions y, = a + cos r and y2 = a + sin z are solutions of the following differential equation y"+y = a. Consider e and oz are two constants. Answer the following. (a) Is cyı +ay2 a solution for a = 1 and e +2 #1? (justify your answer). No points will be given for the answers without justifications. (b) Is Ciy1 +C2½2 a solution for a = 0? (justify your answer). No points will be given for the answers without justifications (c) For a = 0, solve the differential equation with initial condition y(0) = 2 and y(0) = 3.

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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.