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(Solved): a) What can you say about a solution of the equation y^(')=-(1)/(6)y^(2) just by looking at the diff ...



a) What can you say about a solution of the equation

y^(')=-(1)/(6)y^(2)

just by looking at the differf The function

y

must be equal to 0 on any interval on which it is defined. The function

y

must be strictly increasing on any interval on which it is defined. The function

y

must be decreasing (or equal to 0 ) on any interval on which it is defined. The function

y

must be strictly decreasing on any interval on which it is defined. The function

y

must be increasing (or equal to 0 ) on any interval on which it is defined. (b) Verify that all members of the family

y=(6)/((x C))

are solutions of the equation in part (a). We substitute the values of

y

and

y^(')

and test the solution to see if the left hand slide (LHS) it (c) Can you think of a solution of the differential equation

y^(')=-(1)/(6)y^(2)

that is not a member of the

y=e^(6x)

is a solution of

y^(')=-(1)/(6)y^(2)

that is not a member of the family in part (b).

y=0

is a solution of

y^(')=-(1)/(6)y^(2)

that it not a member of the family in part (D).

y=x

is a solution of

y^(')=-(1)/(6)y^(2)

that is not a member of the family in part (b). Every solution of

y^(')=-(1)/(6)y^(2)

is a member of the family in part (b).

y=6

is a solvtion of

y^(')=-(1)/(6)y^(2)

that is not a member of the family in part (b). (d) Find a solution of the initial-value problem.



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