Prove that the general solution of the homogeneous linear system
on the interval (−∞, ∞) is
Want to see the full answer?
Check out a sample textbook solutionChapter 8 Solutions
Bundle: A First Course in Differential Equations with Modeling Applications, Loose-leaf Version, 11th + WebAssign Printed Access Card for Zill's ... Problems, 9th Edition, Single-Term
- Let x=x(t) be a twice-differentiable function and consider the second order differential equation x+ax+bx=0(11) Show that the change of variables y = x' and z = x allows Equation (11) to be written as a system of two linear differential equations in y and z. Show that the characteristic equation of the system in part (a) is 2+a+b=0.arrow_forwardShow that all solutions of the system - (: )- a x' : d approach zero as t → o if and only if a +d 0.arrow_forward5. Let h Ah x = [h₁ + ²√5 h = √5], where h is a real parameter. (a) Find all values of h for which the system X' = AX has either a center, a spiral sink, or a spiral source. (b) Find all values of h for which X' = AX has a sink or a source.arrow_forward
- Prove that the system d dx(t) = −x+4y d = does not have periodic solutions by determining the values of a,n,m so that V (x,y) = xay" is a global Lyapunov function.arrow_forwardSuppose A = system. (0,0,0) (8.2, 3) (2,-1,3) 4 0 -3 (-2,1,-3) (-1,1,1) 5 26 12 -1 4 4 such that Ax = 0. Give a non trivial solution of this homogeneousarrow_forward
- Elements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning