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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
- Suppose 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_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_forward5. Solve the following linear system: dX dt with the initial condition - [83] Y(0) = X [2]arrow_forward
- Consider the linear system ÿ' [₁ 3 -5 -5 2 -3 y.arrow_forward5. Find a general solution of the linear system. x' = 2x + y ly' = x + 2y – e2tarrow_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_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_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_forwardb) Show that Δ2y0 = y2-2y1 + y0.arrow_forward
- 1) 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_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning