Help?? I dont understand Calculus

Question

What logistic equation satisfies this differenatial equation and condition? dy/dt=4y1-(y/24), y(0)=14 pls explain so I can actually understand what's going on in class

Answer 1

the derivative of ayⁿ = n(a)y^n-1

Example:  the derivative of 3y⁴

               = 4(3)y^4-1 = 12y³

 

Taking that in reverse as your question requires:

12y³ had to come from ay⁴ ... 4a=12 so a=3

so the derivative of 3y⁴ = 12y³

 

Also:  The derivative of a constant.. a number

with no variable.. is zero.

 

 dy/dt=4y1-(y/24), y(0)=14...

 

2y² - (1/48)y² + 14

 

dy/dt = 2(2y^2-1) - 2(1/48)y^2-1

 

dy/dt = 4y - (y/24) and y(0) = 14