query 23

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course Mth 279

4/29 1

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:

We can rewrite in the form

y(t) = y_1(t)

y_2(t)

p(t)= (3t)/(t+2) 5/(t+2)

2/(t-2) 4/(t-2)

g(t) = 0

0

t_0 = 1

1

y_0 = 0

2

So for p_11 and p_12 we see function isn’t defined for -2 and for p_21 and p_22 we see function isn’t defined for 2. So we are granuteed the existence of a unique solution on the interval -2

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