Consider the differential equation $\frac { d y } { d t } = y ^ { 3 } - 2 y ^ { 2 } - 15 y$ .(a) What are the equilibrium solutions?
(b) For what values of $y$ is $y ( t )$ increasing?
(c) For what values of $y$ is $y ( t )$ decreasing?
(d) Use the information from above to sketch the direction field for the given differential equation.

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The Answer of Consider the differential equation $\frac { d y } { d t } = y ^ { 3 } - 2 y ^ { 2 } - 15 y$ .(a) What are the equilibrium solutions?
(b) For what values of $y$ is $y ( t )$ increasing?
(c) For what values of $y$ is $y ( t )$ decreasing?
(d) Use the information from above to sketch the direction field for the given differential equation.

Consider the Differential Equation dydt=y3−2y2−15y\frac { d y } { d t } = y ^ { 3 } - 2 y ^ { 2 } - 15 ydtdy​=y3−2y2−15y

Consider the Differential Equation $\frac { d y } { d t } = y ^ { 3 } - 2 y ^ { 2 } - 15 y$