Use the Laplace transform to solve the following initial value problem: y" - y' - 20y= 0, (1) First, using Y for the Laplace transform of y(t), i.e., Y = L(y(t)). find the equation you get by taking the Laplace transform of the differential equation to obtain (2) Next solve for Y = y(0) 9, y(0) 9 0 A (3) Now write the above answer in its partial fraction form, Y + a B 8-b (NOTE: the order that you enter your answers matter so you must order your terms so that the first corresponds to a and the second to b, where a

Q: I want X(s)=

A:

Q: c. write the above answer in its partial fraction decomposition, Y(s) = sq + Y(s) = + d. Now, by…

A:

Q: Use the Laplace transform to solve the following initial value problem: y" - 1y - 30y = 0 y(0) = −4,…

A:

Q: Consider the initial value problem +16y=48t, y(0)=9, (0) = 5. a. Take the Laplace transform of both…

A:

Q: 9

A: a)b) c)

Q: (B Using the Laplace transform, resolve the following differential equation: y' - y = r(t) with…

A:

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

A:

Q: \(d\) is a metric on \(X\). Show that \(\rho : X^2 \to [0,\infty)\) defined by \[ \rho(x,y) =…

A:

Q: Consider the following initial value problem: y′′−4y′−45y=sin(5t)     y(0)=7,y′(0)=5   Using Y for…

A: The given initial value problem,.We have to find the Laplace function using the Laplace transform.

Q: Use the Laplace transform to solve the following initial value problem: y" – 3y = 0, y(0) = 2, y'(0)…

A:

Q: Use the Laplace transform to solve the following initial value problem: y" – 7y' + 10y = 0, У(0) —…

A:

Q: Consider the initial value problem y" + 9y= 18t, y(0) 5, y(0) = 9. = a. Take the Laplace transform…

A: Step 1: Step 2: Step 3: Step 4:

Q: Use the Laplace transform to solve the following initial value problem: y" - 6y - 16y=0 y(0) = 1,…

A:

Q: In this exercise you will use Laplace transforms to solve the differential equation y"+5y'+6y= 0,…

A: (1)let a and b constants , then L(af(t)+bg(t))=aL(f(t))+bL(g(t)).(2) L(eat)=1s−a

Q: Consider the following initial-value problem. y" - 3y' = 8e²t - 2e-t, y(0) = 1, y'(0) = −1 Find…

A: Given- Consider the following initial-value problem.  y'' - 3y' = 8e2t - 2e-t,      y0 = 1, y'0 = -1…

Q: Considel the initial value problem y" – 4y' + 8y = sin(8t) y(0) = 8, y'(0) = 7 A. Use the Laplace…

A:

Q: 8

A: Step 1:Step 2:

Q: Use the Laplace transform to solve the following initial value problem: y" + 16y = 0, y(0) = 8,…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 10

A: Step 1: Step 2: Step 3: Step 4:

Q: Find the Laplace transform of the following differential equation and express it as a single…

A:

Q: L{y(t)} = (s/((s+36)(s^2+36)))+((8+7s)/(s^2+36)) c. Take the inverse Laplace transform of both sides…

A:

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

A:

Q: 11

A: Step 1: Step 2: Step 3: Step 4:

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

A:

Q: Using the linearity of the inverse Laplace transform, solve for the solution of the differential…

A:

Q: t) Consider the following initial value problem: S 7t, 7t, 0 6 Using Y for the Laplace transform of…

A:

Q: y(0) = 1, y'(0) = −2 y" + 8y = 0 First, using Y for the Laplace transform of y(t), i.e., Y =…

A:

Q: the following initial value problem: y" + 36y = S 2t, 0 3 Jsing Y for the Laplace transform of…

A: