Find the general solution of the linear system
x ̇1 = x1, x ̇2 = ax2...
Find the general solution of the linear system
x ̇1 = x1, x ̇2 = ax2
Where a is a constant. Draw the phase planes for a = −1, 0, 1. Comment on the changes of the phase plane
find the general solution of the following as
follows
Xn+2 = -2Xn+1 + 3Xn, x0=1 x1=2
a) find the 2x2 matrix that satisfies Yn+1=AYn
b) Find the characteristic value of A and its corresponding
characteristic vector
c) express X0 = (1 2)as a linear combination of characteristic
vector
d) find Yn
e) find Xn
(A) Find the general solution for the displacement x = x(t) of
the forced mechanical system x´´ + 6x´ + 8x = 35 sin t. (B)
Identify the steady-periodic part
use the elimination method to find the general solution for the
given linear system where differentiation is with respect to t.
2x'+y'-x-2y=e^-t and x'+y'+2x+2y==e^t
Use the elimination method to find a general solution for the
given linear system, where differentiation is with respect to
t.
x'=9x-2y+sin(t)
y'=25x-y-cos(t)
Use the elimination method to find a general solution for the
given linear system, where differentiation is with respect to
t.
x'=5x-6y+sin(t)
y'=3x-y-cos(t)
Find the general solution to the coupled system
dx1 /dt = 2x1
+x2
dx2/dt = x1 +
2x2
Sketch the phase portrait for the system and classify the origin
as a node, a saddle, a center, or a spiral. Is the origin unstable,
asymptotically stable, or stable? Explain and show as much work as
needed
For the linear system x1+3x2=2
3x1+hx2=k
Find values for h and k such that the system has:
a) no solution
b) a unique solution
c) infinitely many solutions