In each of problems 1-12 Solve the given differential equations and the given IVPS. 1. y...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
In each of problems 1-12 Solve the given differential equations and the given IVPS. 1. y (v) +y"=x 2. 16y ) –8y"+ y = 0 (v) 3. У (iv) -Зу +3y "- y" 0 (iv) 4. y =x+e* 6. y"-3y"+3y'-y =-3 sin 5x -3x 7. y"+y'=-2 sin 2x y"+3y"+3y'+y = 30 cosx 9. 4y " +8y"+4ly'+37y = 0, y (0)= 9, y'(0)=-6.5, y"(0)=-39.75 (iv) 10. y) - 16y =128 cosh 2x , y (0) = 1, y'(0)= 24, y" (0)=20, y"(0) =- %3D %3D %3D (iv) 11. y +6y "+17y"+22y'+14y = 0, y (0) = 1, y'(0)=-2, y"(0)=0, y"(0)=3 (iv) "+ y"+8y'-12y =12sinx -e, y (0)= 3, y'(0)= 0, y" (0) =-1, y"(0)= 2 In each of problems 13-14 Determine whether the given set of functions in linearly 12. y ) +2y independent or linearly dependent. 13. fi (x ) =x' +1, f;(x)=x² +x +1, f; (x)=2x -2 14. f, (x )=e*,f2(x )=e*,f:(x )=1 In each of problems 15-17 Solve the given Euler-Cauchy equations. 15. x 'y "+7x 'y"-2xy'-10y = 0, y (1)=1, y'(1)=-7, y"(1) = 44 3 16. х у " +х*у"- 2ху' +2у %3D2х 4 17. х *у " +х *у"- бху'+6у %3D4х ? In each of problems 17-18 Using the method of Variation of Parameters to solve the following equation. 18. y "- y'= x 19. x 'y "+x'y"-2xy'+2y 2x* !! 20. Solve the non-linear equation 2x *(y ")'y" +4x (y")' =y". of In each of problems 1-12 Solve the given differential equations and the given IVPS. 1. y (v) +y"=x 2. 16y ) –8y"+ y = 0 (v) 3. У (iv) -Зу +3y "- y" 0 (iv) 4. y =x+e* 6. y"-3y"+3y'-y =-3 sin 5x -3x 7. y"+y'=-2 sin 2x y"+3y"+3y'+y = 30 cosx 9. 4y " +8y"+4ly'+37y = 0, y (0)= 9, y'(0)=-6.5, y"(0)=-39.75 (iv) 10. y) - 16y =128 cosh 2x , y (0) = 1, y'(0)= 24, y" (0)=20, y"(0) =- %3D %3D %3D (iv) 11. y +6y "+17y"+22y'+14y = 0, y (0) = 1, y'(0)=-2, y"(0)=0, y"(0)=3 (iv) "+ y"+8y'-12y =12sinx -e, y (0)= 3, y'(0)= 0, y" (0) =-1, y"(0)= 2 In each of problems 13-14 Determine whether the given set of functions in linearly 12. y ) +2y independent or linearly dependent. 13. fi (x ) =x' +1, f;(x)=x² +x +1, f; (x)=2x -2 14. f, (x )=e*,f2(x )=e*,f:(x )=1 In each of problems 15-17 Solve the given Euler-Cauchy equations. 15. x 'y "+7x 'y"-2xy'-10y = 0, y (1)=1, y'(1)=-7, y"(1) = 44 3 16. х у " +х*у"- 2ху' +2у %3D2х 4 17. х *у " +х *у"- бху'+6у %3D4х ? In each of problems 17-18 Using the method of Variation of Parameters to solve the following equation. 18. y "- y'= x 19. x 'y "+x'y"-2xy'+2y 2x* !! 20. Solve the non-linear equation 2x *(y ")'y" +4x (y")' =y". of
Expert Answer:
Answer rating: 100% (QA)
1 Solution yx c1 c2x 12x2 2 Solution yx c1e4x c2e2x 3 Solution yx c1 c2x c3x2 4 Solution yx c1 c2x c3ex c4x2 5 Solution yx c1e2x c2e3x 100e3 18e3x2b 6 ... View the full answer
Related Book For
Differential Equations and Linear Algebra
ISBN: 978-0131860612
2nd edition
Authors: Jerry Farlow, James E. Hall, Jean Marie McDill, Beverly H. West
Posted Date:
Students also viewed these mathematics questions
-
In each of Problems 1-2. show that the system is satisfied by the given set of functions. 1. x' = x {x = e' . y = e1} y' = y 2. x' = y (x = sin t, y = cos t) y ' = - x
-
In each of Problems a to c, sketch the graph of the given Cartesian equation, and then find the polar equation for it. a. x - 3y + 2 = 0 b. x = 0 c. y = -2
-
In each of Problems 1 and 2, one of parts (a) and (b) can be integrated with the Power Rule and the other cannot. Integrate the part that can be done with the Power Rule, and explain why the Power...
-
Discuss why you would or would not like to work in an organization like this?
-
A wholesaler encounters a constant demand of 200 cases of one brand and box size of soap flakes per week from his retail accounts. He obtains the soap flakes from the manufacturer at $ 10 per case...
-
Show the products of thesereactions: CH O PhS Na b) Ph,P + CH;CH;CH,Br benzene a) ELOH + CH;I c) CH;CH,CH,CH,S d) NASCH,CH2SNA + BRCH,CH,Br CH
-
Why parties may wish to arbitrate a claim?
-
Weinstein, McDermott, and Roediger (2010) report that students who were given questions to be answered while studying new material had better scores when tested on the material compared to students...
-
Crain Company has a manufacturing subsidiary in Singapore that produces high-end exercise equipment for US. consumers. The manufacturing subsidiary has total manufacturing costs of $1,540,000, plus...
-
Founded in 1972, the German software business SAP (Systems, Applications, and Products in Data Processing) is known as one of the world leaders in enterprise resource planning software, employing...
-
On the excerpt from the example Market Summary report below, which company has the most effective Advertising and PR strategy? Mountain Segment: Product Film Sales Lost Sales Retail Price Awareness...
-
Fiori Corporation's relevant range of activity is 3,100 units to 6,500 units. When it produces and sells 4,800 units, its average costs per unit are as follows: Average Cost per Unit Direct materials...
-
Create and add the VHDL module with two 2 - bit inputs ( x 0 , x 1 , y 0 , y 1 ) , a one bit select input ( s ) , and two - bit output ( m 0 , m 1 ) using structural modeling. A two - bit wide...
-
You can pick a stock whatever you want to answer the questions Go to this site and answer the following questions. https://money.cnn.com/data/markets 1. Pick a stock that's trading on the Market....
-
Please include excel document with regression calculations in your answer Dataset/Reference: https://file.io/xnyC6tLQYgYR Information about the dataset: The data is financial data for 97 companies on...
-
Develop a sustainability plan for using water resources from the country Brazil. This plan should be written with SMART goals (Specific, Measurable, Attainable, Relevant, Time bound). Be clear about...
-
Scenario You are a bookkeeper at a retail company called "Fashion Haven." The company sells trendy clothing and accessories to customers in Australia. The management has asked you to calculate the...
-
Dawson Companys balance sheet information at the end of 2019 and 2020 is as follows: Additional information: The company did not issue any common stock during 2020. Required : Next Level Fill in the...
-
The simplest case of the logistic model is represented by the DE dy/dt = ky( I - y). Where k > 0 is the growth rate constant Draw a direction field for this equation when k = I. Find the constant...
-
(a) Draw a vector field. (b) Draw sample solution curves. (c) Determine the equilibrium points. (d) Determine the stability behavior of the equilibrium points. (e) Discuss the long-term behavior of...
-
Repeal Problem 52, but change the initial volume in tank A to 1 50 gal.
-
A shaft running at \(500 \mathrm{rpm}\) carries a pulley \(1 \mathrm{~m}\) diameter and drives another pulley by means of ropes with a speed ratio of 2:1. The drive transmits \(200 \mathrm{~kW}\)....
-
A flat belt drive is required to transmit \(20 \mathrm{~kW}\) at \(300 \mathrm{rpm}\) of \(2 \mathrm{~m}\) diameter pulley. The angle of contact is \(170^{\circ}\) and coefficient of friction between...
-
If the difference between tight and slack side tensions for a leather belt does not exceed \(100 \mathrm{~N} / \mathrm{cm}\) of width for a belt \(5 \mathrm{~mm}\) thick, find the maximum stress in...
Study smarter with the SolutionInn App