Solve the following differential equation by variation of parameters. Fully evaluate all integrals. y" + 16y = sec(4x). a. Find the most general solution to the associated homogeneous differential equation. Use cj and c, in your answer to denote arbitrary constants, and enter them as c1 and c2. Yc = c1cos(4x)+c2sin(4x) help (formulas) b. Find a particular solution to the nonhomogeneous differential equation y" + 16y = sec(4x). Yp = help (formulas) c. Find the most general solution to the original nonhomogeneous differential equation. Use cj and c2 in your answer to denote arbitrary constants. y = help (formulas)

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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.