Systems of First-Order Differential Equations 333- For each of the following initial value problems determine the la rgest
interval on which there exists a unique solution to the problem.
a. y~ = 3y1 - 2y2
y~ = -y1 + Y2
Y1(0) = 1, Y2(0) = - 1b. y~ = (sinx)y1 + fiy2 + lnx
y~ = (tanx)y1 - exy2 + 1
Initial conditions:(i) Y1(l) = 1, Y2(l) = - 1
c. Y~ = e-xYl - JXTI Y2 + x^2
I Y1Y2 = (x _ 2 )2
Initial conditions:
(i) Y1 (0) = 0, Y2(0) = 1d. Exercise 11 c
e. Exercise 1 l e
f. Exercise llfg. Exercise llg
(ii) Y1(2) = 1, Y2(2) = -1
(ii) Y1(3) = 1, Y2(3) = 0