Question

2. Solve the system of equations using two methods: (1) directly by the eigenvalue method and (2) by elimination method.

(dx/dt)=-2x+y ; (dy/dt)=-2y

Answer #1

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1. Solve the following system of equations by the elimination
method:
2x+y-z=7
x+2y+z=8
x-2y+3z=2
2. Solve the following system of equations by using row
operations on a matrix:
2x+y-z=7
x+2y+z=8
x-2y+3z=2

Use the Laplace transform to solve the given system of
differential equations. 2 dx/dt + dy/dt − 2x = 1
dx/dt + dy/dt − 6x − 6y = 2
x(0) = 0, y(0) = 0

Solve the given system of differential equations by systematic
elimination. 2 dx/dt − 6x + dy/dt = e^t
dx/dt − x + dy/dt = 6e^t

1)Solve the system of linear equations, using the Gauss-Jordan
elimination method. (If there is no solution, enter NO SOLUTION. If
there are infinitely many solutions, express your answer in terms
of the parameters t and/or s.)
x1
+
2x2
+
8x3
=
6
x1
+
x2
+
4x3
=
3
(x1,
x2, x3)
=
2)Solve the system of linear equations, using the Gauss-Jordan
elimination method. (If there is no solution, enter NO SOLUTION. If
there are infinitely many solutions, express...

Use the Laplace transform to solve the given system of
differential equations. dx dt = −x + y dy dt = 2x x(0) = 0, y(0) =
2

Solve the system of linear equations using the Gauss-Jordan
elimination method.
2x
+
2y
+
z
=
7
x
+
z
=
2
4y
−
3z
=
21

Solve the system of differential equations using laplace
transformation
dy/dt-x=0,dx/dt+y=1,x(0)=-1,y(0)=1

Use the Laplace transform to solve the given system of
differential equations. dx/dt=x-2y dy/dt=5x-y x(0) = -1, y(0) =
6

Please show all steps, thank you!
a) Verify that the functions below solve the system:
x(t) = c1e^5t + c2e^-t
y(t) = 2c1e^5t - c2e^-t
Do not solve the system
dx/dt = x + 2y
dy/dt = 4x +3y
b) Solve the system using Operator D elimination. Write the
answer both in scalar and vector form. Please show all steps!
dx/dt = x + 2y
dy/dt = 4x + 3y

Solve the following system of ordinary differential
equations.
2 dx/dt − 2 dy /dt − 3x = e (n+1)t
2 dx/dt + 2 dy/dt + 3x + 8y = 2

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