Use the Laplace transform to find the solution to the differential equation y'' + y =...

Question

Question

Use the Laplace transform to find the solution to the differential equation y'' + y = U(t − 1),

y(0) = 1, y' (0) = 0.

Describe the physical system that this differential equation represents. Plot your solution.

math Advanced-Math

Answer 1

Answer #1

Given y(t)+yL)-1(-1) (1), y(O)-1, y(0)-0 Applying Laplace transform to(1), we get L{y] +L{») = L@c-1)} Lu(t-a)--, a20 where

Answer 2

Similar Homework Help Questions

I need help with this question of Differential Equation. Thanks Find the Laplace transform Y(s) =...

I need help with this question of Differential Equation. Thanks Find the Laplace transform Y(s) = [{y} of the solution of the given initial value problem. 1, 0 <t <t y" + 4y = to, a st<co y(0) = 8, y'(0) = 7
I need help with this question of Differential Equation. Thanks Find the Laplace transform Y(s) =...

I need help with this question of Differential Equation. Thanks Find the Laplace transform Y(s) = [{y} of the solution of the given initial value problem. 1, 0 <t <t y" + 4y = to, a st<co y(0) = 8, y'(0) = 7
1. [5 pts] Unilateral Laplace Transform. Use the unilateral Laplace transform to determine the response of...

1. [5 pts] Unilateral Laplace Transform. Use the unilateral Laplace transform to determine the response of the system described by the following differential equation with the given inputs and initial conditions:LaTeX: \frac{\rm d}{ {\rm d} t } y(t) + \ 10y(t) = \ 10x(t), d d t y ( t ) + 10 y ( t ) = 10 x ( t ) , LaTeX: y(0^-) = 1, x(t) u(t) = u(t). y ( 0 − ) = 1 ,...

Use the Laplace transform to solve the given system of differential equations. Use the Laplace transform...

Use the Laplace transform to solve the given system of differential equations. Use the Laplace transform to solve the given system of differential equations. of + x - x + y = 0 dx + dy + 2y = 0 x(0) = 0, y(0) = 1 Hint: You will need to complete the square and use the 1st translation theorem when solving this problem. x(t) = y(t) =
2. Use the Laplace transform to find a particular solution of the differen- tial equation (as...

2. Use the Laplace transform to find a particular solution of the differen- tial equation (as explained in Example 2). After that, find the solution of the IVP. a) y"+y - 2y = 3t, y(0) = 0, '0) = 1 b) y" +4y=t, y(0) = 1, y(0) = 0
2-Using the Laplace transform find the solution for the following equation d/ at y(t)) + y(t)...

2-Using the Laplace transform find the solution for the following equation d/ at y(t)) + y(t) = f(t) with initial conditions y(0 b Hint. Convolution Dy(0) = a 2-Using the Laplace transform find the solution for the following equation d/ at y(t)) + y(t) = f(t) with initial conditions y(0 b Hint. Convolution Dy(0) = a

1. Use the Laplace transform to convert the following differential equation into s-space and then solve...

1. Use the Laplace transform to convert the following differential equation into s-space and then solve for Y(s): 1/(t) + 14y(t) = sin(34) + cos(5t). 2. Use the Laplace transform to convert the following differential equation into 8-space and then solve for Y(): y") + 3y(t) = (2)
1. Use the Laplace transform to convert the following differential equation into s-space and then solve...

1. Use the Laplace transform to convert the following differential equation into s-space and then solve for Y(s): vy(t) +14y(t) = sin(3) + cos(54) (1) 2. Use the Laplace transform to convert the following differential equation into s-space and then solve for Y(s): "(t) + 3y(t) = 2)
a) Find the general solution of the differential equation Y'(B) + 2y(s) = (1)3 8>0. b)...

a) Find the general solution of the differential equation Y'(B) + 2y(s) = (1)3 8>0. b) Find the inverse Laplace transform y(t) = --!{Y(s)}, where Y(s) is the solution of part (a). c) Use Laplace transforms to find the solution of the initial value problem ty"(t) – ty' (t) + y(t) = te", y(0) = 0, y(0) = 1, fort > 0. You may use the above results if you find them helpful. (Correct solutions obtained without Laplace transform methods...

Solve each differential equation. (Don't use the Laplace transform. 3. IVP: y + cos(x + y)...

Solve each differential equation. (Don't use the Laplace transform. 3. IVP: y + cos(x + y) + (x – y + cos(x + y)) = 0, y(0) = 7. If the equation is exact equation, then solve it. If not, find only an exact equation.