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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?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
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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