(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
ymust be equal to 0 on any interval on which it is defined. The function
ymust be strictly increasing on any interval on which it is defined. The function
ymust be decreasing (or equal to 0 ) on any interval on which it is defined. The function
ymust be strictly decreasing on any interval on which it is defined. The function
ymust 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
yand
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=0is a solution of
y^(')=-(1)/(6)y^(2)that it not a member of the family in part (D).
y=xis 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=6is 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.
