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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_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_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_forward
- 5. Find a general solution of the linear system. x' = 2x + y ly' = x + 2y – e2tarrow_forwardConsider the linear system ÿ' [₁ 3 -5 -5 2 -3 y.arrow_forwardWrite 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_forward
- b) Show that Δ2y0 = y2-2y1 + y0.arrow_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_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
- 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_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_forward4. Solve the system dt -1 with a1 (0) = 1 and 2(0) = -1.arrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning