- #1
SithV
- 5
- 0
Hi people!
This is my first topic here so excuse me if I am doing smth wrong)
So basically I am having problems with understanding of how to sketch
the graphs of solutions of diff. eqs in terms of y and t...
Here is the description and 2 problems:
Problems 8 through 13 involve equations of the form dy/dt = f (y). In each problem sketch
the graph of f (y) versus y, determine the critical (equilibrium) points, and classify each one as
asymptotically stable, unstable, or semistable (see Problem 7).
dy/dt = y(1 − y2), −∞ < y0 < ∞ (1)
dy/dt = y2(1 − y)2, −∞ < y0 < ∞ (2)
so for (1) i have the following:
f(y)=-y3+y and the roots are f(y)=0 then y=0,1,-1.
so for each interval we have:
−∞,-1 (+)
-1,0 (-)
0,1 (+)
1,∞ (-)
which means that -1 and 1 are stable crit. points
and 0 is unstable
I have a cubic parabola for f(y),y plane and i don't know how to interpret all this
data in terms of y,t plane
for (2)
0 and 1 are both semi stable points since the function doesn't change its sign..
same story,cant move to t,y=(
Please help me to understand the idea here!
would be great to see ur sketches=)
Thank u all!
This is my first topic here so excuse me if I am doing smth wrong)
So basically I am having problems with understanding of how to sketch
the graphs of solutions of diff. eqs in terms of y and t...
Here is the description and 2 problems:
Problems 8 through 13 involve equations of the form dy/dt = f (y). In each problem sketch
the graph of f (y) versus y, determine the critical (equilibrium) points, and classify each one as
asymptotically stable, unstable, or semistable (see Problem 7).
dy/dt = y(1 − y2), −∞ < y0 < ∞ (1)
dy/dt = y2(1 − y)2, −∞ < y0 < ∞ (2)
so for (1) i have the following:
f(y)=-y3+y and the roots are f(y)=0 then y=0,1,-1.
so for each interval we have:
−∞,-1 (+)
-1,0 (-)
0,1 (+)
1,∞ (-)
which means that -1 and 1 are stable crit. points
and 0 is unstable
I have a cubic parabola for f(y),y plane and i don't know how to interpret all this
data in terms of y,t plane
for (2)
0 and 1 are both semi stable points since the function doesn't change its sign..
same story,cant move to t,y=(
Please help me to understand the idea here!
would be great to see ur sketches=)
Thank u all!