In Problems 35–46 find the general solution of the given system.
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First Course in Differential Equations (Instructor's)
- Problem 2. i = -x + y – x²? – y² + xy? ý = -y + xy – y² – x²y (1) (2) Determine the values of a for which V (x, y) = x² +ay? is a Lyapunov function for the system.arrow_forwardFind the general solution of the system of D.E. x ¹ 1 (11) 4 १४arrow_forwardProblems 74–77 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam. 74. To graph g(x) = |x + 2| – 3, shift the graph of f(x) = \x| units 76. Solve: logs (x + 3) = 2 units and then 77. Solve the given system using matrices. number Teft/right| number up/down Зх + у + 2z %3 1 75. Find the rectangular coordinates of the point whose polar 2x – 2y + 5z = 5 x + 3y + 2z = -9 coordinates are ( 6, 3arrow_forward
- 2. How many solutions could the following linear system have? ax+by=0 cx + dy=0 ex+fy=0 Give an example of such a system for each possibility.arrow_forward1.3.1 Use elementary operations to solve the system of equations 3x + y = 3 x + 2y = 1.arrow_forward3. Find the general solution of the system given by Y2 + Y3 Y2 = Yı + Y3 (3) Yı + Y2 || || ||arrow_forward
- Please solve the first three parts...arrow_forwardWhich of the following is a solution to the given system of equations found below? (1) x = – /Y %3D (2) y? – x² = 6 O (-v2, 2) O (3, V3) O (-v2, –2) O (-v3, 3)arrow_forwardFind the general solution of the following linear system: [1] 4 3 y' = yarrow_forward
- 2. Given the following 2 x 2 linear system with constant coefficients x' = Ax (H) x= Ax+g(t), (N) where g is not the zero vector. Which of the following statements are true? Justify your answers. A. If , is a solution to (H) and 7, is a solution to (N), then , +27, is a solution to (N). B. If , and 2 are both solutions to (N), then ₁-2 is a solution to (H).arrow_forward[1 1 1] 024. The system of equations | 0 0 1x=| b, | is solvable if |0 0 1 b, (c) b, = b, (d) b, = 0 (e) none (a) h, = b, = 0 (b) b, = b, # 0 025. If A = B+C and B= B' and C' =-C, then %3D %3D (1) C = A– A" »C=÷(4- A') (6) C=;(4+A") (4) C = A+ A" (e) none c=-(4-A') (0) C = (A+ A°) («)C= A+ A°arrow_forwardQ.1. Explain why the linear system has no solution: 1 0 3 1 0 1 2 4 0 0 0 For which values ofk does the system below have a solution? x-3y = 6 + 3z = -3 2x + ky + (3 – k)z = 1arrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning