Concept explainers
In problem 9-14, use Lyapunov’s direct method to determine the stability of the zero solution for the given equation
Want to see the full answer?
Check out a sample textbook solutionChapter 12 Solutions
Fundamentals of Differential Equations and Boundary Value Problems
Additional Math Textbook Solutions
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
Introductory Mathematics for Engineering Applications
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
Excursions in Modern Mathematics (9th Edition)
Discrete Mathematics and Its Applications ( 8th International Edition ) ISBN:9781260091991
- A particular solution of x¨ − 3x˙ + 2x = t2 + 1 is given byarrow_forwardNo. 25 only Show your step-by-step solution.arrow_forwardProblem 6. Solve these nonlinear equations with fsolve function in Matlab. Verify your result with explot function. ƒ₁ (x₁, x₂ ) = X₁ − 4x² − XµX₂ f₂(x₁, x₂)=2x₂-x² – 3x₁ X₂arrow_forward
- Problem 1. The quadratic f = x² + 4xy +2y²2 has a saddle point at the origin, despite the fact that its coefficients are positive. Write f as a difference of two squares.arrow_forward3) Personal taxes Suppose that the percent of total personal income that is used to pay personal taxes is given by y = 0.034x² – 0.044x + 12.642 where x is the number of years past 1990 (Source: Bureau of Economic Analysis, U.S. Department of Commerce). (a) Verify that x = 7 is a solution of 14 = 0.034x² – 0.044x + 12.642. (b) Find the year or years when the percent of total per- sonal income used to pay personal taxes is 14.arrow_forward(13) Prove that the equation x² + 3y² = 2 has no integer solutions.arrow_forward
- (b) To find the daily optimum production number of Portland cement in a factory, one needs to solve the following equations based on the ingredient of cement. The unknowns are lime, x1; silica, x2; alumina, x3; and iron oxide, X4. 10x1 – x2 + 2x3 = 6 -X1 + 11x2 – x3 + 3x4 = 25 2x1 - x2 + 10x3 – X4 = -11 3x2 - x3 +8x4 = 15 Use the Gauss-Seidel iterative technique to find approximate solutions to XỊ, X2, X3, and x4. Starting with x (0, 0, 0, 0)" and iterating until max{]x(*+1) – x(k)} < e = 0.0005arrow_forward2. Show that x4 - 3x - 1 has a solution between 1 and 0, and another solution between 1 and 2.arrow_forward1. Solve 2x-3y-z=0 -x+2y+z=5 3x-4y-z=1arrow_forward
- 1. Solve the following: (a) > 3 5t² – 20 (2) Gabrielle is given the choice of two positions, the first paying $6400 per month and the other paying $4000 per month plus a 5% commission on all sales made during the month. What amount of sale must she make a month for the second position to be more profitable? (3) Create the function which best describes the graph show below. f(x) 8 6- 3- -1- -6 -5 -4 -3 -2 -1 2 3 4 6 8 9 10 11arrow_forwardIn case an equation is in the form y = f(ax+by+c), i.e., the RHS is a linear function of x and y. We will use the substitution = ax + by + c to find an implicit general solution. The right hand side of the following first order problem y = (4x − 3y + 1) 5/6 +, y(0) = 0 is a function of a linear combination of x and y, i.e., y = f(ax +by+c). To solve this problem we use the substitution v= ax + by + c which transforms the equation into a separable equation. We obtain the following separable equation in the variables x and v: U' = Solving this equation an implicit general solution in terms of x, u can be written in the form x+ Transforming back to the variables x and y the above equation becomes x+ = C. y = = C. Next using the initial condition y(0) = 0 we find C = 6 Then, after a little algebra, we can write the unique explicit solution of the initial value problem asarrow_forward2. Find the first three solutions to x² - 22y² = 1 with x and y positive, where the solutions are ordered in terms of increasing order of y value.arrow_forward
- Discrete Mathematics and Its Applications ( 8th I...MathISBN:9781259676512Author:Kenneth H RosenPublisher:McGraw-Hill EducationMathematics for Elementary Teachers with Activiti...MathISBN:9780134392790Author:Beckmann, SybillaPublisher:PEARSON
- Thinking Mathematically (7th Edition)MathISBN:9780134683713Author:Robert F. BlitzerPublisher:PEARSONDiscrete Mathematics With ApplicationsMathISBN:9781337694193Author:EPP, Susanna S.Publisher:Cengage Learning,Pathways To Math Literacy (looseleaf)MathISBN:9781259985607Author:David Sobecki Professor, Brian A. MercerPublisher:McGraw-Hill Education