Distinct Real Eigenvalues
In Problems 1–12 find the general solution of the given system.
11.
Want to see the full answer?
Check out a sample textbook solutionChapter 8 Solutions
A First Course in Differential Equations with Modeling Applications (MindTap Course List)
- 8.2 I only need number 22 pleasearrow_forwardin picarrow_forwardProblem 11. (9.2/22-26) For each of the linear systems in A through E, find the matching phase portrait (to the right). Briefly justify your choices by examining the eigenvalues. A. X(+1)=[-2.5 0.5]x(1) B. X(+1)=[-2.5 0.5]x(1) C. 3 c. dx-[-2.5 0.5]* dx D. [15]* E. dx # - [3 ]x dt 2 1 III o A 2 1- VII O IF 1-2 4 - 110 -1 IV of VI OF -t VIII O -IE I 3arrow_forward
- Problem 1. (Based on Brennan Boyce 2e $3.4 #7) () Consider the 2 x 2 system of ODES, where X(t) = for some real-valued functions x1(t) and x2(t). 4 X(0) = 3 X(t) Do the following: 1. Find the eigenvalues and eigenvectors of A. (Note that these will be complex!). 2. Find the general solution (ignoring initial condition) with real components. 3. Find the particular solution (using the initial condition). 4. Plot each component of the solution as a function of time. 5. Plot the vector plot (i.e. on the X1X2-plane). 6. Using your particular solution, approximate the values of x, (t) and x2(t) (a) when t = (b) when t =2 7. What is the maximum value of x, in the interval 0arrow_forward1. Find the solution to the initial value problem 4x3 + 1 2у — 6 y(1) = 2. A. y = 3 – Vxª + x – 1 B. y = 2+ Vx³ + x – 2 C. y = 1+ Vx4 + x – 1 D. y = 4 – V4x³ + x – 1 E. y = V4³ + x – 1arrow_forwardIn this Problem the Eigenvalues of the coefficient matrix A are given. Find a general solution of the indicated system x’ = Ax.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- 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