In the second case, I have changed the
Growth rate :
$0.7(1-\frac{P(t)}{750})$.
Now I have used the NDSolve to solve the problem
eqn = {P'[t] == 0.7*(1 - P[t]/750)*P[t] - 20}
cond = {P[0] == 30}
sol = NDSolve[{eqn, cond}, P[t], {t, 0, 30}]
Then I calculated the equilibrium points
eqn = 0.7*(1 - P[t]/750)*P[t] - 20;
equilibriumPoints = Solve[eqn == 0, P[t]];
And I have the following plot
p1 = Plot[P[t] /. sol, {t, 0, 20}, PlotStyle -> {Thick, Green}]
Now I am trying to solve with Euler's Method:
sol1 = NDSolve[{P'[t] == 0.7*(1 - P[t]/750)*P[t] - 20, cond}, P[t], {t, 0, 20}, Method -> "ExplicitEuler", MaxSteps -> Infinity]
p2 = Plot[P[t] /. sol1, {t, 0, 30}, PlotStyle -> {Dashed, Red}]
And then I am trying to compare the two solutions
Show[p1, p2, PlotLabel -> "Comparison of Solutions"]
Here it is what I ask for an explanation.