math diff equations

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4 Terms

1
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exponential decay

y’ = k(y-b)

y=Ce^(kx)+b

b is surrounding temp

C = initial difference between surrounding temp and initial temp

2
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logistic growth


|dP/dT = kP(1-P/M)

P = M / (Ae^(-kt)+1)

P=population
k = rate
M = carrying capacity

A = (CARRYING CAPACITY - INITIAL POPULATION) / INITIAL POPULATION
MOPOP

3
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first order linear equation

y’ + P(x) y = Q(x)

y = int( a(x) * Q(x) ) / a(x)
where
a(x) = e^(int P(x))

4
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euler’s method table

x, y, dy/dx, delta y = slope * delta x