Consider the following initial value problem: dy/dt= cube root((y-t) 2 -4) , y(-

Question

Consider the following initial value problem:

dy/dt= cube root((y-t)2-4) , y(-3) = -5.

Since we have

f = ___________is continuous/ not continuous on an open set containing the point (__, __).

and

fy=____________is continuous/ not continuous on an open set containing the point (__,__),

we can apply

The Peano Theorem/ The Picard Lindelof Theorem / or neither

and hence the strongest conclusion that we are able to draw is that

there exists at least one solution / there exists a unique solution / both uniqueness and existence are unclear for solutions

of the given problem (on some interval in t containing the value ____).

Explanation / Answer

f = [((y-t)2-4)]1/3) is continuous on an open set containing the point (_-3,_, _-5_).

fy= 1/3 (((y-t)2-4))-1/3 (is discontinuous on an open set containing the point (_-3,-5_,__),

as (-5-(-3))2 =4 and this expression appears in the denominator

So The Peano Theorem is applicabel and (Picard -Lindelof NOT applicable)

hence the strongest conclusion that we are able to draw is that there exists at least one solution (on some interval in t containing the value ___-3_).

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