Unit Six: Differential Equations

Question 1

Given a differential function, how would you approximate the value of the function given a point and a change in x?

Answer 1

Start with your x and y and their y’, then change in x is given, change in y is old y’ times change in x, new y’ are given by the equation

Question 2

Y is directly proportional to x

Answer 2

Y=kx

Question 3

Y is inversely proportional to x

Answer 3

Y=k/x

Question 4

Y is jointly proportional to x and n

Answer 4

Y=kxn

Question 5

If y is a differentiable function of t such that y>0 and y’=ry for some constant r, then what does y equal?

Answer 5

Pe^rt

Question 6

If y is a differentiable function with constants k and L such that it equals ky(1-y/L), what is the function?

Answer 6

Y=L/1+be^-kt