Question

Find the general solution to the differential equation modeling how a person learns:

????y/????????=100−y.
Then find the particular solutions with the following initial conditions:
y(0)=25 : y=__________________ .
y(0)=120 : y=_________________.
Plot the slope field of this differential equation and sketch the solutions with y(0)=25 and y(0)=120.
Which of these two particular solutions could represent how a person learns?
a. y(0)=25
b. y(0)=120
c. either of these
d. none of the above

Answer 1

Explanation:

`(dy)/(dx) =100-y\\integrating\\y=100y-y^(2) +c\\y(0)=100(0)-0^2+c\\25=c\\so ~y=100~y-y^2+25\\when y(0)=120\\c=120\\y=100~y-y^2+120`