This is the first part of a two-part problem. Rewrite the given system of linear homogeneous differential equations as a homogeneous linear system of the form ?' = P?. y1' = 2y1 + y2 + y3, y2' = y2 + 2y3 + y1, y3' = 2y2 + y1 + y3. ? y1' ? ? ? ? y1 ? | y2' | = | | | y2 | ? y3' ? ? ? ? y3 ?
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Rewrite the given system of linear homogeneous differential equations as a homogeneous linear system of the form y' = Py. y1' = 2y1 + y2 + y3, y2' = y2 + 2y3 + y1, y3' = 2y2 + y1 + y3.
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Rewrite the given system of linear homogeneous differential equations as a homogeneous linear system of the form y' = Py.
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This is the second part of a two-part problem. Show that y(t) is a solution to the system of linear homogeneous differential equations a. Find the value of each term in the equation y1' = 2y1 + y2 + y3 in terms of the variable t. (Enter the terms in the order given.) b. Find the value of each term in the equation y2' = y1 + y2 + 2y3 in terms of the variable t. (Enter the terms in the order given.) c. Find the value of each term in the equation y3' = y1 + 2y2 + y3 in terms of the variable t. (Enter the terms in the order given.)
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