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.