X Your answer is incorrect. Using known Taylor series, find the first four nonzero terms of the Taylor series for the function f (t) = et cost about 0. NOTE: Enter only the first four non-zero terms of the Taylor series in the answer field. Coefficients must be exact. f (t ) = 1+t- + 24 +. . . XFind the particular solution to the differential equation, given the general solution and an initial condition. (C is the constant of integration). :1; = V515 + C; the solution curve passes through (5, 12) y: Current Attempt in Progress Find the value(s) of w for which y = cost satisfies dy + dt2 + 9y = 0. Enter your answers in increasing order. 0 = 0 =Find the value of k for which y = x2 + k is a solution to the differential equation 2y - xy' = 14. k = iFor each differential equation given, select the functions that are solutions. NOTE: Select all that apply. (a) dy -2y dx y = 2 sin x Oy = sin 2x Oy = e22 Dy = e-20 (b) dy = 2y d.x y = 2 sin x Oy = sin 2x Oy = e2:20 Dy = e-2x (c) dy = 4y Oy = 2 sin x y = sin 2x Wy = e2:20 Oy = e-2x (d) dy dac2 -4y Oy = 2 sin x Oy = sin 2x Dy = e2:20 Dy = e-2