(1 point) a. Consider the differential equation: d2y 0.16y-0 dt2 with initial conditions dt (0)-3 y(0)--1 and Find the...
(1 point) Consider the initial value problem d2y dy 8 +41y8 cos(2t), dt dy (0) y(0) = -2 -6 dt dt2 Write down the Laplace transform of the left-hand side of the equation given the initial conditions (sA2-8s+41)Y+2s-18 Your answer should be a function of s and Y with Y denoting the Laplace transform of the solution y. Write down the Laplace transform of the right-hand side of the equation (-8s+32)/(sA2-8s+20) Your answer should be a function of s only...
d2y dy +10 dt +25y 0, y(1) 0, y'(1) 1 (1 point) Solve the initial-value problem dt2 Answer: y(t)
For the system described by the following differential equation d3y(t) d2y(t) d2x(t) dy(t) 3 dt dx(t) 9 dt y(t) 5x(t) 7 2 6 dt3 dt2 dt2 Express the system transfer function using the pole-zero plot technique a) b) What can be said about the stability of this stem? For the system described by the following differential equation d3y(t) d2y(t) d2x(t) dy(t) 3 dt dx(t) 9 dt y(t) 5x(t) 7 2 6 dt3 dt2 dt2 Express the system transfer function using...
Consider the differential equation y" – 7y + 12 y = 0. (a) Find r1, 72, roots of the characteristic polynomial of the equation above. 11,2 M (b) Find a set of real-valued fundamental solutions to the differential equation above. yı(t) M y2(t) M (C) Find the solution y of the the differential equation above that satisfies the initial conditions y(0) = -4, y'(0) = 1. g(t) = M Consider the differential equation y" – 64 +9y=0. (a) Find r1...
(1 point) Consider the initial value problem d'y dy dt2 dt dt Write down the Laplace transform of the left-hand side of the equation given the initial conditions Your answer should be a function of s and Y with Y denoting the Laplace transform of the solution y Write down the Laplace transform of the right-hand side of the equation Your answer should be a function of s only. Next equate your last two answers and solve for Y. You...
Consider the differential equation y" + 8y' + 15 y=0. (a) Find r1 r2, roots of the characteristic polynomial of the equation above. = 11, 12 M (b) Find a set of real-valued fundamental solutions to the differential equation above. yı(t) M y2(t) M (C) Find the solution y of the the differential equation above that satisfies the initial conditions y(0) = 4, y(0) = -3. g(t) = M (10 points) Solve the initial value problem y" - 54' +...
Required information Consider the following equation: dạy dt2 +9y=0 Given the initial conditions, 10) = 1 and y(0) = 0 and a step size = 0.1. Solve the given initial-value problem from t= 0 to 4 using Euler's method. (Round the final answers to four decimal places.) The solutions are as follows: t y z 0.1 1.2 2.3 4
(1 point) Solve the following differential equation with the given boundary conditions -If there are infinitely many solutions, use c for any undetermined constants - If there are no solutions, write No Solution - Write answers as functions of 2 (ie.y=y(2)). y" +9y=0 • A) Boundary conditions: y(0) = 2 • B) Boundary conditions: y(0) = 2 y= No Solution • C) Boundary conditions: y(0) = 2 No Solution
1.46 Find the solution for M(d2y/dt2) + C(dy/dt) + Mg 0. Show that this represents the motion of a body rising with drag proportional to velocity
(1 point) Consider the differential equation This equation has the 2 constant solutions (in increasing order) y -3 and y= The solution of this equation subject to the initial condition y(O)9 is y- (1 point) Consider the differential equation This equation has the 2 constant solutions (in increasing order) y -3 and y= The solution of this equation subject to the initial condition y(O)9 is y-