Use a computer algebra system to draw a direction field for the differential equation y' = 2y3 − 2y. Get a printout and sketch on it solutions that satisfy the initial condition y(0) = c for various values of c. For what values of c does the limit L = lim t → [infinity] y(t) exist?

d.) yes, because the volume of the cone is greater than the volume of the sphere

step-by-step explanation:

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb

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