Module - Mathenatical modelling Question 1: 10 Marks(1.1)By using an analytical approach (do not use inspection as marks will be deducted), determineall the equilibrium point(s)of the following differential equation:dxdt=5(x2-12)-1-2(x2-12)-3Question 2: 30 MarksDraw the phase lines of the following differential equations. List all the equilibrium points for each system,and classify them as stable or unstable:dxdt=e2ln(x)+5elnx-36dxdt=1-sin(x)dxdt=eln(xlogx)-x3104Question 3: 26 MarksFor each of the following systems,dxdt=-11x(3.2)dxdt=(x2-11x),(3.3)dxdt=(-2x2+4x-2)(x3+2x2+x)Draw the sketch of:(a)dxdtas a function ofx,(b) the phase line,(c) also, for each system, list all the equilibrium points and classify each of them as stable orunstable,(d) and predict the outcome of the solution if the system starts atx(0)=-1.Question 4: 20 MarksConsider the modeldPdt=7P+14P2where P(t) represents the size of the population at time t.(4.1)Is this a logistic model? Justify your answer!(4.2) Draw a phase line of the model.(4.3) Draw a sketch of the solution curve P(t),ifP(0)=7.Question 5: 14 MarksAssume that for the systemdxdt=G(x)a graph of the function G looks like this:(5.1) Draw a rough graph of what the function G(x) could look like.(5.2) Draw a rough sketch of the solution curves x(t) when the initial value isx(0)=1 and whenthe initial value isx(0)=0.