## Answers

Given that the differential equation is y" - 18y'+82y= 26t+t sin (27) - COS(2+) (1) Equation (1) is a 2nd order linear non-homogeneous differential equation. Therefore the general solution of the differektial equation & in y (t) = Y c (t) + Up (t) where ye (t) is the complementary function of the corres ponding homogeneous differential equation of (1) and yo(t is the particular solution of (1). The homogeneous differential equation of 4) is y" -- 18y'+82y=0 Let Yc (t) = emt be any solution of differential equa (2) "Yé = memt mremt since ye(t) is a solution of (2), we have ya -1896 +829€ = 0.

M-18 -18m +82) emtzo, (: Ye=emt Ye=ment y elment m 18m+82-0, ( emt+o) This is a quadratic equation in m. So we have 18 & J (18) 2 4x82 → Żm ma 2 2 1821324-328 18+ 34 2 18 +255 2. = gti, izni 1.

.. The complimentary fimetion of (2) is Yelt) = est(acos (t) + G sin (t), G, and q being arbitrary constants.

.
We see that the terms in the right hand side. of the differential equation (1) does not involve in the complimentary function Yc (t) for the root m= 9 ti, so by method of undetermined coefficients wwe take the particulas solution of the form +(B+Ct) (F Sin (2+)+G WS(21)) +(H cos(20+ L sin (2) where A, B, C, F, G, H and L are constants to be determined . ... The form of the particular solution of equa (1) is ypte= (Aest (B+C(F Sin (2+ G cos (ex+ (Hcos (21)+Lsio (10 Yp (t) = Ae6t

#### Similar Solved Questions

1 answer

##### B) Who has the comparative advantage in the production of good B? a. Alex b. Adam c. Both Alex and Adam d. Neither Alex...

b) Who has the comparative advantage in the production of good B? a. Alex b. Adam c. Both Alex and Adam d. Neither Alex nor Adam Alex Adam Good A Good A Good B 0 160 30 Good B 300 225 150 75 0 120 80 25 50 75 100 60 90 40 120 a) Who has the comparative advantage in the production of good A? a. Alex ...

1 answer

##### Regarding the distribution of sample means which of the following statements is false the standard error of distributi...

regarding the distribution of sample means which of the following statements is false the standard error of distribution of sample means is a measure of the average distance of each sample mean from the larger population the distribution of sample means shows how smaller sample means are distribut...

1 answer

##### 29. A pump is tested in the laboratory and the following data were obtained: Fluid =...

29. A pump is tested in the laboratory and the following data were obtained: Fluid = water Rotational speed = 300 rpm Head difference = 8 ft Volume flow rate = 10 gpm Impeller diameter = 4 in. The impeller is changed to one whose diameter is 3-1/2 in., and the pump is run at 900 rpm. Find the new vo...

1 answer

##### Plzz help Exercise 4-7 Process Costing Journal Entries (L04-1) Chocolaterie de Geneve, SA, is located in...

plzz help Exercise 4-7 Process Costing Journal Entries (L04-1) Chocolaterie de Geneve, SA, is located in a French-speaking canton in Switzerland. The company makes chocolate truffles that are sold in popular embossed tins. The company has two processing departments-Cooking and Molding. In the Cookin...

1 answer

##### The Neptune Company offers network communications systems to computer users. The company is planning a major...

The Neptune Company offers network communications systems to computer users. The company is planning a major investment expansion but is unsure of the cost of equity capital as it has no publicly-traded equity. Your assignment is to determine an appropriate equity cost. List and explain the steps yo...

1 answer

##### E6D.3(b) Calculate the standard potential of the cell Pt(s) cystine(aq), cysteine(aq)|| H*(aq)|O2(g)|Pt(s) and the standard Gibbs...

E6D.3(b) Calculate the standard potential of the cell Pt(s) cystine(aq), cysteine(aq)|| H*(aq)|O2(g)|Pt(s) and the standard Gibbs energy of the cell reaction at 25°C. Use EⓇ =-0.34 V for cystine(aq) + 2 H+(aq) + 2e → 2 cysteine(aq)....

1 answer

##### In-Class Activity #4 Circular Flow Diagram: A: B: F: G: H: D: what is the value for "I" in the circular flow diagram, if A-$10, B-$25, С = 12, D-ss, and E-57? In-Class Activity #4 Ci...

In-Class Activity #4 Circular Flow Diagram: A: B: F: G: H: D: what is the value for "I" in the circular flow diagram, if A-$10, B-$25, С = 12, D-ss, and E-57? In-Class Activity #4 Circular Flow Diagram: A: B: F: G: H: D: what is the value for "I" in the circular flow diagram, ...

1 answer

##### The cash records and bank statement for the month of July for Glover Incorporated are shown...

The cash records and bank statement for the month of July for Glover Incorporated are shown below. GLOVER INCORPORATED Cash Account Records July 1, 2021, to July 31, 2021 Cash Balance July 31, 2021 $6,930 Cash Balance July 1, Cash 2021 + Receipts $6,790 $8,180 Cash Receipts Date Desc. 7/9 Sales 7/21...

1 answer

##### You have three variables: response variable=income and the predictor variables are years of college (measured in...

You have three variables: response variable=income and the predictor variables are years of college (measured in years) and years of experience (measured in years). Would you use ANOVA, Linear regression, or Logistic regression in this situation and why?...

5 answers

##### Please assist me in answer this question please show me all the formulas used and the units and how to convert them if needed

Please assist me in answer this question please show me all the formulas used and the units and how to convert them if needed. Thank You. If the half-life of Ba (140, 56) is 12.75 dyas, how many atoms of (140, 56) Ba will be left after 9 weeks if there were initially 2.4 mol of atoms? How do I do...

1 answer

##### 16)A triangular conducting loop lies in a uniform magnetic field B which varies with time as...

16)A triangular conducting loop lies in a uniform magnetic field B which varies with time as shown in 10 the graph. At t = 1 s the magnetic field is pointing out of the page. The triangle's height is-3 ma ptsFor what time interval(s) is the induced current in the loop equal to zero? (b) During w...

1 answer

##### 19. + 2/6 points Previous Answers OSAtomsChem1 7.4.P.060. The following quantities are placed in a container....

19. + 2/6 points Previous Answers OSAtomsChem1 7.4.P.060. The following quantities are placed in a container. 2.01x1024 atoms of hydrogen, 1.29 mol of sulfur, and 118.1 g of diatomic oxygen (a) What is the total mass in grams for the collection of all three elements? 49 162.8 g (b) What is the total...

1 answer

##### Accounting

If a revenue expenditure is treated as a capital expenditure, thena. expenses are overstated and assets are overstated.b. expenses are overstated and owners' equity is understated.c. net income is overstated and owners' equity is understated.d. expenses are understated and owners' equity...

1 answer

##### Pure oxygen gas was first prepared by heating mercury(II) oxide, HgO: 10.72 2 HgO(s)-? 2Hig(I) +...

Pure oxygen gas was first prepared by heating mercury(II) oxide, HgO: 10.72 2 HgO(s)-? 2Hig(I) + 02(g) What volume in liters of oxygen at STP is released by heating 10.57 g of HgO? 10.73 How many grams of HgO would you need to heat if you wanted to prepare 0.0155 mol of O2 according to the equation ...

1 answer

##### Your task is to process a file containing the text of a book available as a...

Your task is to process a file containing the text of a book available as a file as follows: A function GetGoing(filename) that will take a file name as a parameter. The function will read the contents of the file into a string. Then it prints the number of characters and the number of words in the ...

1 answer

##### Explain the importance of audience demographics. Describe why audience analysis is important and how it can...

Explain the importance of audience demographics. Describe why audience analysis is important and how it can affect or change your presentation. How might the audience demographics change with a change in geographic location--be specific, providing details to support your ideas. When replying to peer...

1 answer

##### A government issues $4000000 of serial bonds paying interest at j2 = 9%, of which $2000000...

A government issues $4000000 of serial bonds paying interest at j2 = 9%, of which $2000000 is redeemed in 10 years, $2000000 is redeemed in 15 years and $0 is redeemed in 20 years. Determine the purchase price on the day that the bonds were issued, in order for investors to receive a yield of j2 = 4...

1 answer

##### A solution of Lici in water is 22.0 wt% LiCl. What is the mole fraction of...

A solution of Lici in water is 22.0 wt% LiCl. What is the mole fraction of Lici? O 0.120 O 0.107 4.33 O 0.519 QUESTION 22 Identify the set of hybrid orbitals shown below. OOOO sp O sp2 O sp3 304...

2 answers

##### What are all values for A between 0-360 degrees? sin^2(A/2)=cos^2A

What are all values for A between 0-360 degrees? sin^2(A/2)=cos^2A...