Question

Write the general solutions of the advancement operator equations:

Give a particular solution for (A-12) (A+3) (A-12)h = 0

Answer #1

Which of the following systems of equations have nonzero
solutions? If the solution is not unique, give the set of all
possible solutions.
a)3x+4y=0 b)4x-y=0 c)2x-6y=0
6x+2y=0 4x-y=0 -x+3y=-2

The system of equations may have a unique solution, an infinite
number of solutions, or no solution. Use matrices to find the
general solution of the system, if a solution exists. (If there is
no solution, enter NO SOLUTION. If there are infinitely many
solutions, express your answers in terms of z as in
Example 3.)
3x
?
2y
+
5z
=
11
2x
?
3y
+
4z
=
8

how can i write all possible automorphism of field
Q(√2,√3)?is there any general equations ?please give me the steps
of the answers

2. Solve for the general and definite solutions for the
following difference equations:
yt+1=-0.5yt +3, y0
=1
yt+2= yt+1-2yt+12,
y0=4, y1=5

Find the general solutions for the following differential
equations:
a. (D^2 - 8D + 16)y = 0
b. (D^4 - 9D^3)y = 0

Find the particular solutions yp of the following
EQUATIONS using the Method of Undetermined Coefficients. Primes
denote the derivatives with respect to x.
y''-y'-6y=29sin(3x)
y''-5y'+8y=xex
Solve for the particular solution of both equations!

3. Find the general solution to each of the following
differential equations.
(a) y'' - 3y' + 2y = 0
(b) y'' - 10y' = 0
(c) y'' + y' - y = 0
(d) y'' + 2y' + y = 0

Use Gauss-Jordan elimination to solve the following systems of
linear equations, or state that there are no solutions.
a)
4?+8?=−4
−3?−6?=5
b)
?+4?−?=8
2?+8?+?=1
you should find that the system has infinitely many solutions.
Introduce a parameter in order to give the general solution. Then
give one particular solution.

4. Find a particular solution, and the general solution to the
associated homogeneous equation, of the following differential
equations:
a) y'-2y=6
b) y'+y=3e-t

y'''+2y''-4y'+8y= -5cos(x)-10sin(x)+16e2x
A.Solve the underlining homogenous equation, solve the
characteristic equations, write fundamental solutions
B. Find the particular solution? (use undetermined coefficients
method to find particular solution)

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