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(2 points) Consider the initial value problem -,[0 1 y 1 0 -4...
_ [2 sin(t) o (0)-5.5 a. Form the complementary solution to the homogeneous equation e(-t) 5e (t)...
Part A is already done.
_ [2 sin(t) o (0)-5.5 a. Form the complementary solution to the homogeneous equation e(-t) 5e (t) + c2 en(-t) en(t) b. Construct a particular solution by assuming the form p(t) (sin t)ã + (cos t)band solving for the undetermined ja + (cost)¡ and solving for constant vectors ã and B. Ep(t)- c. Form the general solution ¢(t) (t) + zp(t) and impose the initial condition to obtain the solution of the initial value problem...
Consider the initial value problem: 2' - 2+ 2(0) = (*) a. Form the complementary solution...
Consider the initial value problem: 2' - 2+ 2(0) = (*) a. Form the complementary solution to the homogeneous equation. -e (t) = 21 +02 b. Construct a particular solution by assuming the form zp(t) = ae+ bt+c and solving for the undetermined constant vectors a, b, and c. 2p(t) = c. Solve the original initial value problem. 31(t) ) - 22(0)
(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...
(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...
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...
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" + 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" +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...
(1 point) In this exercise you will solve the initial value problem e-9 y" – 184'...
(1 point) In this exercise you will solve the initial value problem e-9 y" – 184' +81y = 4472; y(0) = -3, v'(0) = -2. (1) Let C and Cybe arbitrary constants. The general solution to the related homogeneous differential equation y" – 18y' +81y = 0 is the function yh() = C1 yı() + C2 y2() = C1 +C2 NOTE: The order in which you enter the answers is important; that is, Cif(T) + C29(2) #C19() +C2f(). is of...
(1 point) Solve the Bernoulli initial value problem - 2 'y', y(1)=2 For this example we...
(1 point) Solve the Bernoulli initial value problem - 2 'y', y(1)=2 For this example we haven We obtain the equation + given by Solving the resulting first order linear equation for u we obtain the general solution with arbitrary constant Then transforming back into the variables 2 and y and using the initial condition to find C Finally we obtain the explicit solution of the initial value problem as
Part A is already done.
_ [2 sin(t) o (0)-5.5 a. Form the complementary solution to the homogeneous equation e(-t) 5e (t) + c2 en(-t) en(t) b. Construct a particular solution by assuming the form p(t) (sin t)ã + (cos t)band solving for the undetermined ja + (cost)¡ and solving for constant vectors ã and B. Ep(t)- c. Form the general solution ¢(t) (t) + zp(t) and impose the initial condition to obtain the solution of the initial value problem...
Consider the initial value problem: 2' - 2+ 2(0) = (*) a. Form the complementary solution to the homogeneous equation. -e (t) = 21 +02 b. Construct a particular solution by assuming the form zp(t) = ae+ bt+c and solving for the undetermined constant vectors a, b, and c. 2p(t) = c. Solve the original initial value problem. 31(t) ) - 22(0)
(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...
(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...
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...
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" + 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" +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...
(1 point) In this exercise you will solve the initial value problem e-9 y" – 184' +81y = 4472; y(0) = -3, v'(0) = -2. (1) Let C and Cybe arbitrary constants. The general solution to the related homogeneous differential equation y" – 18y' +81y = 0 is the function yh() = C1 yı() + C2 y2() = C1 +C2 NOTE: The order in which you enter the answers is important; that is, Cif(T) + C29(2) #C19() +C2f(). is of...
(1 point) Solve the Bernoulli initial value problem - 2 'y', y(1)=2 For this example we haven We obtain the equation + given by Solving the resulting first order linear equation for u we obtain the general solution with arbitrary constant Then transforming back into the variables 2 and y and using the initial condition to find C Finally we obtain the explicit solution of the initial value problem as
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