Differential Equations Concepts

Question 1

Main points for separable equations

Answer 1

1. y’ = R(x) / L(y)
2. integral of L(y)dy = integral of R(x)dx

Question 2

y’ = k(y-b) -> ?

Answer 2

y = b + Ce^(kt)

Question 3

Newton’s Law of Cooling = ?

Answer 3

T(t) = Ts + (To - Ts)e^(-kt)

Question 4

Euler’s Method for slope fields

Answer 4

1. x_(n+1) = x_n + h
2. y_(n+1) = y_n + H*F(x_n,y_n)

Question 5

Formulae for Logistic Equations?

Answer 5

1. dy/dt = ky(1-(y/A))
2. y=A/(1-(e^(-kt)/C))
3. C = y0/(y0-A)