Question: Consider the initial value problem y + 16y = 48t, y(0) = 7, /(0) = 2. a. Take the Laplace transform of both sides

Consider the initial value problem y" + 16y = 48t, y(0) =

Consider the initial value problem y" + 16y = 48t, y(0) = 7, /(0) = 2. a. Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of y(t) by Y(s). Do not move any terms from one side of the equation to the other (until you get to part (b) below). help (formulas) b. Solve your equation for Y(s). Y(s) = L {u(t)} = c. Take the inverse Laplace transform of both sides of the previous equation to solve for y(t). y(t) !!

Step by Step Solution

★★★★★

3.42 Rating (149 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Given the differential equation a ytt dt 16 yt 48 t Apply the Laplace transformation both s... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Consider the initial value problem y + p ( x ) y = q ( x ) , y ( x 0 ) = y 0 , where p ( x ) and q ( x ) are continuous on some open interval I . (a) Use the method of variation of parameters to...

Given is the solution to the initial value problem Y = AY. Y(0) = Y0 (a) Show that (b) Let x = (x1,...,x,,)and c = (c1,...,cn)T. Assurning that the vector x1...,xn are linearly independent, show that...

Consider the initial value problem y =y+2x-x, y(0) =1 with exact solution v(x) = x +e*. If step size 0.15896 0.3496 0.04% O 0.0013%

Consider the initial value problem (solution: y = 1/[2.5 - S(x)] + 0.01x 2 where S(x) is the Fresnel integral (38).(a) Solve (17) by Euler, improved Euler, and RK methods for 0 ? x ? 5 with step h =...

Use Eulers method with step size to compute the approximate -values of the solution of the initial value problem yt = y - 2x, y(1) = 0.

Apply the multistep method in Prob. 23 to the initial value problem y' = x + y, y(0) = 0, choosing h = 0.2 and doing 5 step. Compare with the exact values.

In Exercises 3-6, solve the initial value problem x'(t) = Ax(t) for t > 0, with x(0) = (3, 2). Classify the nature of the origin as an attractor, repeller, or saddle point of the dynamical system...

(a) Write down an integral formula for the solution to the initial value problem du/dt = Au + b. u(0) = 0. dt where b is a constant vector. (b) Suppose b mg A. Do you recover the solution you found...

Use Eulers method to solve the initial value problem graphically, starting at x 0 = 0 with a. dx = 0.1. b. dx = -0.1. dy dx x + y ey + xy(0) = 0

Use Eulers method to solve the initial value problem graphically, starting at x 0 = 0 with a. dx = 0.1. b. dx = -0.1. dy 1 dx ex+y+2, y(0) = = -2

Oriole Corporation incurred the following transactions. 1 2 3:4. 5. Manufacturing overhead costs incurred on account were$88,550. Depreciation on the company's office building was $8,880.7. Manufac...

Pets-R-Us Adjusted Trial Balance 31-Dec-23 Accounts Debit Credit Cash $165,000 Accounts Receivable 130,100 Inventory 39,500 Land 67,300 Buildings 120,000 Accumulated Depreciation 10,400 Accounts...

Five districts make up a province with a 60- seat congress. District populations are given below. Use Jefferson's method to apportion the seats to the districts. How many seats go to District C?...

Sophie is the HIM director at Medical Center of Alabama. The Medical Center of Alabama is part of a five-hospital chain and two health clinics known as Hometown Health. Sophie earned her RHIA five...

2.18 Given the following project (all times are in days Activity Predecessor Normal time Normal cost Crash time Crash cost A 3 $40 2 $80 B A 2 20 1 80 C A 2 20 2 20 D A 4 30 1 120 E B 3 10 1 80 a....

John's accounting firm has been receiving backlash for its lack of inclusivity. John is frustrated with the feedback. John intentionally recruits in diverse neighborhoods and his staff is racially...

P 6 - 1 A ? A ( a ) Make up and solve an original problem to illustrate the principles of this chapter. See Problem P 4 - 1 A for guidelines. ( b ) Write a question based on the material in this...

QUESTION 9 HC-O-C-R R-C-O-CH HC-O-P-O-CH-CH-NH3* O || O a. Phosphatidic acid, Serine O b. Lysophosphatidic acid, Serine, Free FA O c. Lysophosphatidylserine, Free FA O d. 2 Free FAs, Serine, Glycerol...

Apply the maximum likelihood method to the normal distribution with = 0.

Show that in a network G with all cij = 1, the maximum flow equals the number of edge-disjoint paths s t.

(a) The Fibonacci numbers are recursively defined by a 0 = a 1 = 1, a n+1 + a n + a n-1 if Find the limit of the sequence (a n+1 /a n .) (b) Fibonaccis rabbit problem. Compute a list of a 1 , a 12 ....

1. There are many ways to describe feeling sad and depressed. In your culture, what are different idioms for expressing feelings of sadness and depression (such as feeling blue or down in the dumps)?...

2. Say you wanted to find out about the gestures of a particular culture and their meaning. How would you go about doing that research? How would you know for sure thats what people actually did when...

1. How do you define good health for yourself? Does your definition resemble the WHO definition of health? Does it incorporate other aspects of health that are not mentioned in the WHO definition?