sir steve plz am a little confuse

Question

(x-y)³=A(x+y)
prove that (2x+y)dy/dx=x+2y

if y is a function of x and x=e^t/(e^t+1) show that dy/dt=x(1-x)dy/dx

plz explain to me very well sir damon answered that but i still dont get it
If u want me to show my work i will do it sir plz plz help
also i tried all that but i dont just gett

Answer 1

we have
3(x-y)^2 (1-y') = A + Ay'
3(x-y)^2 - 3(x-y)^2 y' - A'y = A
(3(x-y)^2 + A)y' = -(A+3(x-y)^2)
y' = -1
so, y = -x and

(2x+(-x))(-1) = (x + 2(-x))
-x = -x
Kind of a strange problem.

Now for the other one, I'm not sure I can improve on Damon's solution.

dy/dt = dy/dx * dx/dt
= dy/dx * (e^t/(e^t+1)^2)
= dy/dx * (e^t/(e^t+1))/(e^t+1)
= dy/dx * x/(e^t+1)

Now, 1/(e^t+1) = (1+e^t-e^t)/(e^t+1)
= (1+e^t)/(e^t+1) - e^t/(e^t+1)
= 1-x

So,

dy/dt = dy/dx * x(1-x)

Answer 2

k i just practise that now and i got
dy/dx=(3(x-y)^2-A)/(A+3(x-y)^2)

how did u get dy/dx=-1

plz explain

Answer 3

and also what happen to the orther e^t+1

becus u have x/e^t+1
and in conclusion u said
x(1-x)

Answer 4

okay i think i understand now thanks you are good