Question

Calculus conceptual question

Answer 1

ok

Answer 2

If y(x) is a solution to dy/dx = 2y(5=y) with y(0) = 3,
then as x approaches infinity,

a. y(x) increases to infinity
b. y(x) increases to 5
c. y(x) decreaes to 5
d. y(x) decreases to 2
e y(x) decreases to 0

I think it's a because the derivative only depends on y and it's 5y which is always positive. Is that right?

Answer 3

dy/dx = 2y(5-y) *

Answer 4

separate the variables and integrate ,

find the constant of integration with the initial value

Answer 5

And that constant is what the function increases/decreases to?

Answer 6

basically dy/dx = f(y)

Answer 7

so its not dependant on x

Answer 8

its invariant wrt to x

Answer 9

you would need partial fractions if you solve by seperation of variables