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= )x-12

Question

DIFFERENTIAL EQUATIONS

Refer to the given 3x3 coefficient matrix with initial conditions (see attached image). Find the particular solution to the initial value problem.

= )x
-12
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= )x -12

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Step 1

To solve we have to find eigen vectors for this we have to find eigen values.

To find eigen values,

Take determinate

Then,

[1-2-12
-14
0-
--(1)
2 2
-3
-2-2
-2+2-252+25
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[1-2-12 -14 0- --(1) 2 2 -3 -2-2 -2+2-252+25

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Step 2

Solving above equation we can get

Now,

A= 1,+5i,-5i
Eigen vector for A=1 is found by substituting A=1in the (1) and reducing to echelon form we
get 2=1
-12
-14
-12
-14
2-1
-3
1
-2-1
1
1
help_outline

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A= 1,+5i,-5i Eigen vector for A=1 is found by substituting A=1in the (1) and reducing to echelon form we get 2=1 -12 -14 -12 -14 2-1 -3 1 -2-1 1 1

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Step 3

Reducing to echelon form

Now eigen...

0
0 1
0 0
-25
Z
Put Z 6
Z
Z
25
-7
6
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0 0 1 0 0 -25 Z Put Z 6 Z Z 25 -7 6

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