When solving a differential equation using the Laplace transform, you apply the Laplace transform to both sides of the equation and then solve for Y(s) before applying the inverse Laplace transform. Find Y (s) for the initial value problem y" – 5y' + 6y = h(t – 1) with y(0) = 1 and y'(0) = 0. s+5 O Y = e (s-3)(s-2) (s-3)(8–2) s+1 O Y = - s(s-3)(s-2) (s-3)(s-2) e (s-1) (8-1)(s-3)(s-2) 8-5 Y = + (s-3)(s-2) 1 OY e s(s–3)(s–2) + (s-3)(8-2) O Y = + (8-3)(s-2) 8-5 s(8-3)(s-2)

Q: Question 4 く Given the differential equation 6t y''+ 4y = 9e", y(0) = 0, y'(0) = 0 %3D Apply the…

A:

Q: y" +6y' + 4y = 10e ; y(0) = 0, y'(0) = -2 Answer: y = et -e-t +e-* 3

A: We are given the differential equation : y''+6y'+4y=10et Taking Laplace transform both sides, we…

Q: Consider the following initial value problem: x" 5x14x = sin(8t), x(0) = 2, x' (0) = -1. Using X for…

A: In your answer this will be 696 place of 632

Q: Recall that the differential equation for the instantaneous charge q(t) on the capacitor in an…

A:

Q: Consider the initial value problem +36-cos(64), (0) - 6, (0) 3. a Take the Laplace transform of both…

A:

Q: Transform the differential equation y" +10y" - 25y' - 250y=9e-t y(0)=0 y' (0) = 0 y" (0) = 1 into an…

A:

Q: Solve the differential equation using Laplace transform of y" - 3y' + 2y = e3t ; when y(0) =0 and…

A: To Solve: y''-3y'+2y=e3t; when y0=0 and y'0=0 Concept: Let Lyt=Ys be any given Laplace TransformThen…

Q: xy" – 2(x + 1)y' + (x + 2)y = 0.

A:

Q: Consider the following initial value problem: x" - 5x²14x = sin(8t), x(0) = 2, x' (0) = -1. Using X…

A: We will use Laplace transformation table  f't  = s Fs− f0f'' t= s2 Fs − s f0 − f0Lsinat=aa2+s2

Q: Consider the differential equation 2y" + ty' - 2y = 18, y(0) = y'(0) = 0. In some instances, the…

A: Given differential equation is 2y''+ty'-2y=18 Also given y0=y'0=0   To Solve: The first-order DE for…

Q: Construct a Sign Chart for the following polynomial function and state the intervals where this…

A: The given polynomial function is fx=-23-2xx-32x2+1. Determine the intervals where fx is positive and…

Q: b. Determine whether the statement is true or false and justify your answer. Determine which of the…

A:

Q: Use the Laplace transform to solve the following initial value problem: y' + 8y = 0 y(0) = 3, y(0) =…

A:

Q: Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below. y'' -…

A: Our objective is given below:

Q: Consider the following initial value problem. у" + 8y' + 25y %3D 8(t — п) + 8(t - 7л), у(0) 3D 1,…

A:

Q: Consider the following initial value problem: y" ly 30y = sin(7t) Using Y for the Laplace transform…

A:

Q: Consider the following initial-value problem. y' - y = 2 cos(4t), y(0) = 0 Find {f(t)} for f(t) = 2…

A: Solution :-

Q: Consider the following initial value problem: x(0) = 2, x' (0) = -1. Using X for the Laplace…

A:

Q: y" — y' = 2x, y (0) = 1, y'(0) = -2

A:

Q: 7y" +46y" 175y' - 1150y = 4e t y(0) = 0 y (0) 0 y" (0) = 1 into an algebraic equation by taking the…

A:

Q: x' + 3x = 9t, x(0) = 4. Take the Laplace transform of both sides of the given differential equation…

A:

Q: . Determine the Laplace transform of the differential equation 3y" – y' = et5 - 9y" + 4y

A:

Q: Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below.…

A: Given initial value problem

Q: Consider the following initial value problem: x" – 2x' – 24x = sin(7t), x(0) = 5, x'(0) = -1. Using…

A: Given differential equation is

Q: Use the Laplace transform to solve the following initial value problem: x' = 13x +5y, y = -8x + est…

A:

Q: Transform the differential equation 9y" +14-81 - 126y= 5et y(0) = 0 3/(0) = 0 3'(0) = 1 into an…

A:

Q: Question 1 Use Laplace Transform technique to solve the initial value problem y' + 2y = 26 sin 3t ,…

A:

Q: When solving a differential equation using the Laplace transform, you apply the Laplace transform to…

A:

Q: y" + 5y' + 4y = e³t ;y(0) = 0, y'(0) = 1

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.