Consider the following differential equation. (A computer algebra system is recommended.) (1 + t2)y' + 4ty = (1 + t2)−2 (a) Draw
a direction field for the given differential equation.
1 answer:
Answer:
Step-by-step explanation:
a. Draw a direction field for the given differential equation
b. Based on the inspection of the direction field, describe ow solutions behave for large t.
The solution appear oscillatory
All solutions seems to converge to the function y0(t)=4
All solutions seems to converge to the function y0(t)=0
All solutions seems to seems to eventually have negative slopes a and hence decrease without bound
All solutions seems to seems to eventually have positive slopes a and hence increase without bound
C
As t-infinity
All solutions seems to seems to eventually have positive slopes a and hence decrease without bound
All solutions seems to converge to the function y0(t)=0
All solutions seems to seems to eventually have negative slopes a and hence decrease without bound
All solutions seems to converge to the function y0(t)=4
The solution are oscillatory
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You can substitute the value of y(5/6 x + 1) from the first equation for y in the second and get 
which becomes 
and you get
Least to Greatest:
2/10, 2/5, 1/2, 5/3
Explanation:
They are all different fractions.
Hopefully, this helps! :D
Practice with the number line!
For this case we have that the inverse variation is defined as:
Where:
k: It is the constant of proportionality
According to the statement we have:
We find the constant of proportionality:
Then we find the value of x when :
Answer: