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course MTH-279

08/03 around 10:45 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?

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

y1’ = 3ty/t+2 + 5y2/t+2 - undefined at -2

y2’ = 2y1/t-2 + 4y2/t-2 - undefined at 2

so,

(-infinity, -2)

(-2, 2) largest interval

(2, infinity)

Confidence rating: 3

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Given Solution:

Self-critique (if necessary): OK

Self-critique rating: OK

*********************************************

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?

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

Confidence rating:

y(t) = [y1(t); y2(t); y3(t)] = [y(t); y’(t); y’’(t)]

-----

-2y1 + 4y3 + e^3t

-2y + 4y’’ + e^3t = y’’’

y’’’ + 2y - 4y’’ = e^3t

y’’’ - 4y’’ + 2y = e^3t - higher order equation

.............................................

Given Solution: 2,3

Self-critique (if necessary): OK

Self-critique rating: OK