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(1 point) Given the fourth order homogeneous constant coefficient equation y' + 10y" + 9y =...
(3 points) Given the fourth order homogeneous constant coefficient equation y"" + 10y" + 9y-0 1)...
(3 points) Given the fourth order homogeneous constant coefficient equation y"" + 10y" + 9y-0 1) the auxiliary equation is ar br3+ cr2 + dr +e 2) The roots of the auxiliary equation are (enter answers as a comma separated list) 3) A fundamental set of solutions is Enter the fundamental set as a commas separated list yi , y2,y, y4). Therefore the general solution can be written as ycy c232 +c3ys c4y4- 4) Use this to solve the IVP...
(1 point) Given the third order homogeneous constant coefficient equation y" + 3y" + 3y +...
(1 point) Given the third order homogeneous constant coefficient equation y" + 3y" + 3y + y = 0 1) the auxiliary equation is ar3 + br2 + cr + d = ^3+3r^2+3r+1 - = 0. 2) The roots of the auxiliary equation are -1,-1,-1 (enter answers as a comma separated list). 3) A fundamental set of solutions is e^(-x),xe^(-x),x^2e^(-x) (enter answers as a comma separated list). 4) Given the initial conditions y(0) = -1, ý (0) = 2 and...
(1 point) We consider the non-homogeneous problem y" – y'=1 – 10 cos(2x) First we consider...
(1 point) We consider the non-homogeneous problem y" – y'=1 – 10 cos(2x) First we consider the homogeneous problem y" – y' = 0; 1) the auxiliary equation is ar? + br +c= = 0 2) The roots of the auxiliary equation are (enter answers as a comma separated list). (enter answers as a comma separated list). Using these we obtain the the complementary solution yc = Ciyi + C2y2 for arbitrary 3) A fundamental set of solutions is constants...
(1 point) We consider the initial value problem 4xy" + 4xy' +9y = 0, y1) =...
(1 point) We consider the initial value problem 4xy" + 4xy' +9y = 0, y1) = 1, y'(1) = -3 By looking for solutions in the form y = x" in an Euler-Cauchy problem Ax?y' + Bxy + Cy = 0, we obtain a auxiliary equation Ar2 + (B – A)r + C = 0 which is the analog of the auxiliary equation in the constant coefficient case. (1) For this problem find the auxiliary equation: = 0 (2) Find...
(1 point) We consider the non-homogeneous problem y" + 4y = -32(3x + 1) First we...
(1 point) We consider the non-homogeneous problem y" + 4y = -32(3x + 1) First we consider the homogeneous problem y" + 4y = 0: 1) the auxiliary equation is ar? + br +c= r^2+4r = 0. 2) The roots of the auxiliary equation are 0,4 (enter answers as a comma separated list). (enter answers as a comma separated list). Using these we obtain the the complementary 3) A fundamental set of solutions is 1,e^(-4x) solution yc = cyı +...
(1 point) We consider the non-homogeneous problem y" - y' = -4 cos(x) First we consider...
(1 point) We consider the non-homogeneous problem y" - y' = -4 cos(x) First we consider the homogeneous problem y -y = 0 : = 0 1) the auxiliary equation is ar2 + br + c = 2) The roots of the auxiliary equation are (enter answers as a comma separated list) 3) A fundamental set of solutions is (enter answers as a comma separated list). Using these we obtain the the complementary solution ye = ciyı + c2y2 for...
We consider the non-homogeneous problem y' = 30(18x – 2x4) First we consider the homogeneous problem...
We consider the non-homogeneous problem y' = 30(18x – 2x4) First we consider the homogeneous problem y'' = 0 : 1) the auxiliary equation is ar2 + br +c= = 0. 2) The roots of the auxiliary equation are (enter answers as a comma separated list). 3) A fundamental set of solutions is (enter answers as a comma separated list). Using these we obtain the the complementary solution yc = C1y1 + C2y2 for arbitrary constants ci and C2- Next...
(1 point) We consider the non-homogeneous problem y" +2y +2y 20os(2x) First we consider the homogeneous...
(1 point) We consider the non-homogeneous problem y" +2y +2y 20os(2x) First we consider the homogeneous problem y" + 2y' +2y 0 1) the auxiliary equation is ar2 br 2-2r+2 2) The roots of the auxiliary equation are i 3) A fundamental set of solutions is eAxcosx,e xsinx (enter answers as a comma separated list). (enter answers as a comma separated list). Using these we obtain the the complementary solution yc-c1Y1 + c2y2 for arbitrary constants c1 and c2. Next...
We consider the non-homogeneous problem y" + 2y + 2y = 40 sin(2x) First we consider...
We consider the non-homogeneous problem y" + 2y + 2y = 40 sin(2x) First we consider the homogeneous problem y" + 2y + 2y = 0: 1) the auxiliary equation is ar? + br +C = 242r42 = 0. 2) The roots of the auxiliary equation are 141-14 Center answers as a comma separated list). 3) A fundamental set of solutions is -1 .-1xco) Center answers as a comma separated list. Using these we obtain the the complementary solution y...
(8 pts) In this problem you will solve the non-homogeneous differential equation y" + 9y =...
(8 pts) In this problem you will solve the non-homogeneous differential equation y" + 9y = sec (3x) (1) Let C and C2 be arbitrary constants. The general solution to the related homogeneous differential equation y" + 9y = 0 is the function yn (x) = C1 yı(2) + C2 y2(x) = C1 +C2 NOTE: The order in which you enter the answers is important; that is, Cif(x) + C2g(x) + C19(x) + C2 f(x). (2) The particular solution yp(x)...
(3 points) Given the fourth order homogeneous constant coefficient equation y"" + 10y" + 9y-0 1) the auxiliary equation is ar br3+ cr2 + dr +e 2) The roots of the auxiliary equation are (enter answers as a comma separated list) 3) A fundamental set of solutions is Enter the fundamental set as a commas separated list yi , y2,y, y4). Therefore the general solution can be written as ycy c232 +c3ys c4y4- 4) Use this to solve the IVP...
(1 point) Given the third order homogeneous constant coefficient equation y" + 3y" + 3y + y = 0 1) the auxiliary equation is ar3 + br2 + cr + d = ^3+3r^2+3r+1 - = 0. 2) The roots of the auxiliary equation are -1,-1,-1 (enter answers as a comma separated list). 3) A fundamental set of solutions is e^(-x),xe^(-x),x^2e^(-x) (enter answers as a comma separated list). 4) Given the initial conditions y(0) = -1, ý (0) = 2 and...
(1 point) We consider the non-homogeneous problem y" – y'=1 – 10 cos(2x) First we consider the homogeneous problem y" – y' = 0; 1) the auxiliary equation is ar? + br +c= = 0 2) The roots of the auxiliary equation are (enter answers as a comma separated list). (enter answers as a comma separated list). Using these we obtain the the complementary solution yc = Ciyi + C2y2 for arbitrary 3) A fundamental set of solutions is constants...
(1 point) We consider the initial value problem 4xy" + 4xy' +9y = 0, y1) = 1, y'(1) = -3 By looking for solutions in the form y = x" in an Euler-Cauchy problem Ax?y' + Bxy + Cy = 0, we obtain a auxiliary equation Ar2 + (B – A)r + C = 0 which is the analog of the auxiliary equation in the constant coefficient case. (1) For this problem find the auxiliary equation: = 0 (2) Find...
(1 point) We consider the non-homogeneous problem y" + 4y = -32(3x + 1) First we consider the homogeneous problem y" + 4y = 0: 1) the auxiliary equation is ar? + br +c= r^2+4r = 0. 2) The roots of the auxiliary equation are 0,4 (enter answers as a comma separated list). (enter answers as a comma separated list). Using these we obtain the the complementary 3) A fundamental set of solutions is 1,e^(-4x) solution yc = cyı +...
(1 point) We consider the non-homogeneous problem y" - y' = -4 cos(x) First we consider the homogeneous problem y -y = 0 : = 0 1) the auxiliary equation is ar2 + br + c = 2) The roots of the auxiliary equation are (enter answers as a comma separated list) 3) A fundamental set of solutions is (enter answers as a comma separated list). Using these we obtain the the complementary solution ye = ciyı + c2y2 for...
We consider the non-homogeneous problem y' = 30(18x – 2x4) First we consider the homogeneous problem y'' = 0 : 1) the auxiliary equation is ar2 + br +c= = 0. 2) The roots of the auxiliary equation are (enter answers as a comma separated list). 3) A fundamental set of solutions is (enter answers as a comma separated list). Using these we obtain the the complementary solution yc = C1y1 + C2y2 for arbitrary constants ci and C2- Next...
(1 point) We consider the non-homogeneous problem y" +2y +2y 20os(2x) First we consider the homogeneous problem y" + 2y' +2y 0 1) the auxiliary equation is ar2 br 2-2r+2 2) The roots of the auxiliary equation are i 3) A fundamental set of solutions is eAxcosx,e xsinx (enter answers as a comma separated list). (enter answers as a comma separated list). Using these we obtain the the complementary solution yc-c1Y1 + c2y2 for arbitrary constants c1 and c2. Next...
We consider the non-homogeneous problem y" + 2y + 2y = 40 sin(2x) First we consider the homogeneous problem y" + 2y + 2y = 0: 1) the auxiliary equation is ar? + br +C = 242r42 = 0. 2) The roots of the auxiliary equation are 141-14 Center answers as a comma separated list). 3) A fundamental set of solutions is -1 .-1xco) Center answers as a comma separated list. Using these we obtain the the complementary solution y...
(8 pts) In this problem you will solve the non-homogeneous differential equation y" + 9y = sec (3x) (1) Let C and C2 be arbitrary constants. The general solution to the related homogeneous differential equation y" + 9y = 0 is the function yn (x) = C1 yı(2) + C2 y2(x) = C1 +C2 NOTE: The order in which you enter the answers is important; that is, Cif(x) + C2g(x) + C19(x) + C2 f(x). (2) The particular solution yp(x)...
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