(1 point) Note WebWork will interpret acos(x) as cos ¹(x), so in order to write a times cos(x) you need to type a * cos(

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1 Point Note Webwork Will Interpret Acos X As Cos X So In Order To Write A Times Cos X You Need To Type A Cos 1 (81.09 KiB) Viewed 9 times

(1 point) Note WebWork will interpret acos(x) as cos ¹(x), so in order to write a times cos(x) you need to type a * cos(x) or put a space between them. The general solution of the homogeneous differential equation can be written as where a, b are arbitrary constants and is a particular solution of the nonhomogeneous equation y" +9y=0 NOTE: you must use a, b for the arbitrary constants. Find the solution satisfying the initial conditions Yc = a cos(3x) + b sin(3x) Ур = e²x y" +9y = 13e² By superposition, the general solution of the equation y" +9y = 13e²¹ is y = Yc + Yp SO y = a cos(3x)+bsin(3x)+e^(2x) y(0) = -2, y' (0) = 2 -3cos(3x)+(2/3)sin(3x)+e^(2x) The fundamental theorem for linear IVPS shows that this solution is the unique solution to the IVP on the interval (-inf,inf) The Wronskian W of the fundamental set of solutions cos(3x) and sin(3x) of the homogeneous equation is W = 3