a. b. Solve the IVP -5 3 [= il (x1+[ 6te *) (O)=(-1) -3 Solve the IVP 79 [] = [-* ?] [?]+[6] [70] = [4] 1 0
2. Let Y = ex2, where X ~ Ņ(0, 1). (a) Find the p.d.f. of Y. J0 oPlY2 > ijdt. (b) C ompuite 2. Let Y = ex2, where X ~ Ņ(0, 1). (a) Find the p.d.f. of Y. J0 oPlY2 > ijdt. (b) C ompuite
2. Consider the IVP /" -+13y-6(t-2), (o)-o,)-1 a. Solve the IVP. b. Find the exact value for the following.
solve the IVP using the Laplace approach ï + 2 i + 5 x = e-3t, x(0) = 1, *(0) = 0
(1) Give the general solutions of the following DE and solve the IVP. (a) 42y" 3zy 3y 82/3, given that e C +C223/4 (b)(5 )y-5y2e-5*, y(0)-1,(1/5)-2, given that e (5z -1)G2e- (1) Give the general solutions of the following DE and solve the IVP. (a) 42y" 3zy 3y 82/3, given that e C +C223/4 (b)(5 )y-5y2e-5*, y(0)-1,(1/5)-2, given that e (5z -1)G2e-
a.) Solve the following IVP. X !=3x,-13x2 X, (O)=3 X2 = 5x +X2 X₂(0)=-10 b.) solve the following IVP. X;= -X, +(3/2) X2 X, (2)=1 X 2 = (-%6) xx-2x2 X2 (2)=0
1. Let k be an integer. Solve the following: (b) ;-164+3 (c) (754-3)(-+1) 2. Solve each of the following equations for : (a) 21 - 5iz = 2zi (b) 49 + 22 = 0 (c) 2 = 2(i-5) (d) := (1 - 2)(1 - 41) (e) : + zi + 12 = 0 3. Solve the linear system of equations: 21 + iz2 = -1 21 - 22 = i 4. Draw plots for the regions described by the following...
The following IVP will be used for Question 1 and Question 2 on this quiz. Solve the initial value problem using the method of Laplace Transforms. y' - y' = 6x y(0) = 2,y'(0) = -1 The solution will be accomplished through answering the two questions below. In using the Laplace Transform to solve the above IVP, solving for Y(s) gives Y(8) = Y(s) = + 8+3 $-2 s-2 Y(s) – + 5 $+2 8-3 3 5 Y(s) = +...
(3) Solve the IVP + 6y(t) + 9 Sy()dt = 1, y(0) = 0. (4) Find a(t) that satisfies e(t) = e-t +S* sinh(t – 7)2(7) dt.
Please answer #3 Problem 3: Find a solution to the IVP dy dy + dc2 + y = 0, y(0) = y'(0) = 1. dx Problem 4: Suppose you are given the differential equation ay" +by' + cy = 9(2) where a, b, and c are constants. For each of the following choices of g(x), write down the form for the particular solution Yp that you would use: (a) g(x) = 205 (b) g(x) = x²e32 (c) g(x) = xº...