Question

dy/dx=y^(3)-2y^(2)-15y
what the constant solution to the differential equation?
what values of y is y(x) increasing? decreasing?
use the information from above to sketch the direction field for the given differential equation.

Answer 1

this is very similar to : dy/dx=y^(2)-4y+3

Answer 2

use the same method as that post

Answer 3

I'm confused about that one too><

Answer 4

Constant Solutions:
y is constant when: \(dy/dx=0\)

\[\large \therefore y^3-2y^2-15y=0\]

Answer 5

-3<y<0, y>5 increasing?

Answer 6

y<-3,0<y<5 decreasing?

Answer 7

yes

Answer 8

How about the sketch?

Answer 9

.... using dashed lines