dPdt=kP(1−PM)(1−mP)) dPdt=kP(1−PM)(1−mP) Solve this differential equation using separation of variables. Only separate the equations and integration (not solving for P) M= carrying capacity (maximum value) m= threshold value (minimum value) k= the proportionality constant

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dPdt=kP(1−PM)(1−mP)) dPdt=kP(1−PM)(1−mP)  Solve this differential equation using separation of variables. Only separate the equations and integration (not solving for P) M= carrying capacity (maximum value) m= threshold value (minimum value) k= the proportionality constant

unett · Accepted Answer

Given:  The differential equation is  dpdt=kP(1−pm)(1−mp)   he given differential euation can be written as,  dpdt=k(M−PM(P−MP)   dPdt=k(M−Pm)(p−m))   dp(M−P)(P−m)=kdtm)   Integrate the above expression.  ∫(dp(M−P)(P−m))∫kmdt−−−−1  Now,  1(M−P)(P−m)=AM−p)+BP−m   A(P−m)+B(M−P)(M−p)(P−m))   P(A−B)+(bm−Am)(M−p)(P−m))   Compare both sides  A−B=0)   A=B)   And,  BM−Am)   A(M−m)=1)  So,   B=1M−m   Substitute the values in eq---1  1M−m)∫1M−pdp+1M−n∫1P−mdp=∫kmdt   1M−m)[−∈(M−P)+∈(p−m)]=ktm+c   Inp−mM−p)=(ktm+C)(M−m)

dP/dt = kP(1-P/M)(1-m/P))dP/dt = kP(1-P/M)(1-m/P) Solve this differential equation using

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