Consider the nonhomogeneous linear equation y" +9y' g(t) with the complementary solution y,= c1y1(t) + czy2(t) + caya(t). By the method of Variation of Parameters, a particular solution of the nonhomogeneous equation is of the form y, = u1 (t)y1(t) + u2 (t)y2(t) + u3(t)y3(t). Find the equation satisfied by the function u, (t). O a. (t) =-9(t) cos 3t O b. (t) = g(t) sin 3t Oc (t) = 9(t) cos 3t O d. (t) = -9(t) sin 3t

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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.