In Problems 31 and 32, solve the given initial-value problem and give the largest interval I on which the solution is defined. dy 32. + 2(t + 1)y? = 0, y(0) = 8. dt 33. (a) Without solving, explain why the initial-value problem dy

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In Problems 31 and 32, solve the given initial-value problem
and give the largest interval I on which the solution is defined.
dy
32.
+ 2(t + 1)y² = 0, y(0)
8.
dt
33. (a) Without solving, explain why the initial-value problem
dy
Vy, y(xo) = Yo»
dx
%3D
has no solution for yo < 0.
(b) Solve the initial-value problem in part (a) for yo > 0
and find the largest interval I on which the solution is
defined.
Transcribed Image Text:In Problems 31 and 32, solve the given initial-value problem and give the largest interval I on which the solution is defined. dy 32. + 2(t + 1)y² = 0, y(0) 8. dt 33. (a) Without solving, explain why the initial-value problem dy Vy, y(xo) = Yo» dx %3D has no solution for yo < 0. (b) Solve the initial-value problem in part (a) for yo > 0 and find the largest interval I on which the solution is defined.
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