query 23

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course Mth 279

8/6 4:50 pm

Query 23 Differential Equations*********************************************

Question:  What is the largest interval over which the solution to the system

(t + 2) y_1 ' = 3 t y_1 + 5 y_2

(t - 2) y_2 ' = 2 y_1 + 4 y_2

with initial conditions

y_1(1) = 0

y_2(1) = 2

is defined?

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Your solution: 

 rewriting equations

y1' = 3t/(t+2) y1 + 5/(t+2) y2

y2' = 2/(t-2) y1 + 4/(t-2) y2

cannot be at -2 or 2 and must include 1

(-2, 2)

 

 

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Given Solution: 

 

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Self-critique (if necessary):

 

 

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Question:  The equation

y ' = [ y_2; y_3; -2 y_1 + 4 y_3 + e^(3 t) ]

with initial condition

y(0) = [1; -2; 3]

represents a higher-order equation of form

y[n] + a_(n-1) * y[n-1] + ... + a^2 y '' + a_1 y ' + a_0 y = g(t).

(y[n], for example, represents the nth derivative of y; a_(n-1) is understood as a with subscript n - 1).

What is the higher-order equation?

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Your solution: 

 y' = [y'; y''; y''']

y''' = 4y'' - 2y + e^(3t)

y'(0) = 1

y''(0) = -2

y'''(0) = 3

 

 

confidence rating #$&*:

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Given Solution: 

 

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Self-critique (if necessary):

 

 

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Self-critique rating:

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