Finding the limit and a differential equation

[cokezero]

i can't seem to figure this out...

if the differential equation dy/dx= y-2y^2 has a solution curve y=f(x) contianing point (0, 0.25) , then the limit as x approaches infinity of f(x) is



a)no limit

b. 0

c. 0.25

d. 0.5

e. 2


i usually just separate the variables and find f(x) then take the limit, but i can't seem to find f(x) b/c it would require the integral of 1/(y-2y^2)

 

[Data]

i usually just separate the variables and find f(x) then take the limit, but i can't seem to find f(x) b/c it would require the integral of 1/(y-2y^2)

so, integrate $\frac{1}{y-2y^2}$! Partial fractions will do it.

 

[cokezero]

yeah i know...
i get the equation

y= 1/(e^-x + 2) +C
without the c value it is 1/2 for the limit
but with the c value which is -1/12 i get a limit of 5/12 which is not an answer choice...

so the question becomes, does the limit depend on the c value or not?

 

[Data]

That's not the answer I get for y(x). Try checking your work again. If you still can't figure it out, post what you've done and I'll try to tell you what's wrong!