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In Problem 1 –6 , classify the critical point at the origin of the given linear system.
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Fundamentals of Differential Equations and Boundary Value Problems
- 5. Solve the following linear system: dX dt with the initial condition - [83] Y(0) = X [2]arrow_forward2. Determine whether the systems below are linear and/or time invariant. Be sure to show your work. a. y(t) = 3x (t) + 1 b. +ty(t) = x (t) c. + 2y(t) = 3 d. y(t) = x(T) dr e. y(t) = x(7) dtarrow_forwardSuppose are solutions to a 2-dimensional linear system el dx = A(t)x + f(t). dt (a) Find the general solution of this system. (b) Find A(t) and f(t).arrow_forward
- Write the given linear system without the use of matrices. (1)-(1)-·-(-)) -t + 2 e 2 X d - D y. dt 1 Z 8 dx dt dy dt dz dt || = )-(-3 1 -1 9 X -6 -2 5 y 3arrow_forwardIndicate which of the statement(s) below is(are) true: (a) y(t) = 3 x(t) is a linear expression %3D (b) y(t) = r(t+2) is a causal system %3D (c) y(t) = K- (t – 2) is memoryless and causal %3D O a. All of them are TRUE O b. (a) is the only TRUE statement O c. (a) and (b) are TRUE O d. (b) and (c) are TRUEarrow_forward1) Write down the general solution of the following linear systems. Draw the phase planes. - 2y y' = 3x - 6y а) x' = x - x' = x + 2y y' = 5x - 2y b) c) x' = -3x + 2y y X 2y b) y X' = 6x y - 3 7х — 2уarrow_forward
- (B. Janssen, KTH, 2014) Consider the linear system 0.550x+0.423y = 0.127 0.484x + 0.372y = 0.112 Suppose we are given two possible solutions, u = [_11] and v- -1.91. 1.01 0.9 a. Decide based on the residuals b - Au and b - Av which of the two possible solutions is the 'better' solution. b. Calculate the exact solution x. c. Compute the errors to the exact solution. That is, compute the infinity norms of u-x and v-x. Do the results change your answer to 7a?arrow_forward6. Consider the dynamical system dx - = x (x² − 4x) - dt where X a parameter. Determine the fixed points and their nature (i.e. stable or unstable) and draw the bifurcation diagram.arrow_forwardConsider the following system x = (a 1¹ ) x + (1₁) ₁ U (2) Find the values of a so that the system is stable, or asymptotically stable?arrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning