c0043ce0-7a47-4329-9b90-b8e63e5c15bb 6 9 12 decimal

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DE Verhulst [Logistic]

a k t f 1 y a y - (* / y int k t int ≡ y solve maple :

a k t f a k t * a * exp * 1 k t * a * exp + /

a k y0 t f1 1 u a u - (* / u y0 y int k u 0 t int ≡ y solve maple :

a k y0 t f1 y0 a * k t * a * exp * a y0 1 - k t * a * exp + (* + /

k y0 t0 t f2 1 u 1 u - (* / u y0 y int k u t0 t int ≡ y solve maple :

k y0 t0 t f2 y0 k t t0 - (* exp * 1 y0 1 - k t t0 - (* exp + (* + /

a k y0 t0 t f3 1 u a u - (* / u y0 y int k u t0 t int ≡ y solve maple :

a k y0 t0 t f3 y0 a * k a * t t0 - (* exp * a y0 1 - k a * t t0 - (* exp + (* + /

r to yo t Logistic 111 yo / 1 - (r t to - (* - exp * + / :

r 1 : yo 0.5 : to 10 : ε 0.75 : 14 mat

r to yo x Logistic r to ε - yo x Logistic r to ε + yo x Logistic to yo + 15 black 1 5 mat 4 1 sys

Otherwise solve integral equalities

a k u t f u y a y - (* / y int k t int ≡ y solve maple :

u ii el a 1 k j el t i el * a * u ii el / exp + / ln * k j el t i el * a * + u ii el / exp

a k u t f u a 1 k t * a * u / exp + / ln * k t * a * + u / exp

u 1 u 2^+ / u 1 y int u sin - u 0 t int ≡ y solve maple 21 t cos - (* exp 2 - 21 t cos - (* exp + (* - sqrt 21 t cos - (* exp / 21 t cos - (* exp 2 - 21 t cos - (* exp + (* - sqrt 21 t cos - (* exp / - 21 mat

u 1 u 2^+ / u 1 y int u sin - u 0 t int ≡ t solve maple 1 y 2^+ ln 2 / 2 ln 2 / - 1 + acos