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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

Respuesta :

Answer:

Step-by-step explanation:

[tex]\frac{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[/tex]

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