Question

Consider the linear system

dY/dt=(0 2 −2 −1)Y

(a) Find the general solution.

(b) Find the particular solution with the initial value

Y0=(−1,1).

Answer #1

Consider the following linear system (with real eigenvalue)
dx/dt=-2x+7y
dy/dt=x+4y
find the specific solution coresponding to the initial values
(x(0),y(0))=(-5,3)

Find the general solution of the system
dx/dt = 2x + 3y
dy/dt = 5y
Determine the initial conditions x(0) and y(0) such that the
solutions x(t) and y(t) generates a straight line solution. That is
y(t) = Ax(t) for some constant A.

Consider the differential equation. Find the solution y(0) =
2.
dy/dt = 4t/2yt^2 + 2t^2 + y + 1

Find the general solution to the system:
dx/dt = -4x + 3y
dy/dt = -5x/2 + 2y

Find the general solution to the following:
[(e^t)y-t(e^t)]dt+[1+(e^t)]dy=0

Find the general solution of the equation.
d^2y/dt^2-2t/(1+t^2)*dy/dt+{2/(1+t^2)}*y=1+t^2

Consider the following initial value problem:
dy/dt = -3 - 2 *
t2, y(0) = 2
With the use of Euler's method, we would like to find an
approximate solution with the step size h = 0.05 .
What is the approximation of y
(0.2)?

consider the simplified linear
system system,
dS/dt= -αI
dI/dt= αI
For α > 0, find the
general solution of this linear system, and sketch the phase
portrait. Also, briefly explain how increasing α
influences solutions in this linear model.

Consider the differential equation y′′+ 9y′= 0.(
a) Let u=y′=dy/dt. Rewrite the differential equation as a
first-order differential equation in terms of the variables u.
Solve the first-order differential equation for u (using either
separation of variables or an integrating factor) and integrate u
to find y.
(b) Write out the auxiliary equation for the differential
equation and use the methods of Section 4.2/4.3 to find the general
solution.
(c) Find the solution to the initial value problem y′′+ 9y′=...

dy/dt = x- (1/2)y
dy/dt =2x +3y
a)matrix form
b)find eigenvalues/eigenvectors
c)genreal solution

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