erential equations, use phase flow, ial conditions, indicate x and y Iclines and equilibria. (if needed) Solve x=A, y=Bt+C with A, B, and C constants.
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- Van der Waals Equation In Exercise 18 at the end of Section 2.3, we discussed the ideal gas law, which shows the relationship among volume V, pressure p, and temperature T for a fixed amount 1 mole of a gas. But chemists believe that in many situations, the van der Waals equation gives more accurate results. If we measure temperature T in kelvins, volume V in liters, and pressure p in atmosphere 1 atm is the pressure exerted by the atmosphere at sea level, then the relationship for carbon dioxide is given by p=0.082TV0.0433.592V2atm What volume does this equation predict for 1 mole of carbon dioxide at 500 kelvins and 100 atm?Suggestion: Consider volumes ranging from 0.1 to 1 liter.Differential equiations Select a system of linear equations from any science of your choice, describe it clearly, develop its solution, determine its stability, critical points and phase planes. Based on the result, make observations of the phenomenon studied. Please be as clear as possible, and legible. Show and explain all the steps. Thank you very much.initial condition of the system of equations : x(0)=0, y(0)=0, z(0)=0, f(0)=0. Solve with gauss seidel method.Tolerance=0.2 (Consider 8 digits after the comma.) What are the x, y, z, f values in the first interaction where the error limit is provided? 10x-y+2z=14 -x+11y-z+3f=30 2x-y+f-z=26 3y-z+8f=35
- Modeling with first order differential linear equations: A tank contains 100 gallons of water and 50 oz of salt. water containing a salt concentration of 1/4(1+1/2sint) oz/gal flows into the tank at a rate of 2 gal/min, and the mixture in the tanks flows out at the same rate. a. find the amount of salt in the tank at any time.Second Order Homogeneous Linear EquationsThe system of differential equations dx/dt = 0.4x − 0.002x2 − 0.001xy dy/dt = 0.6y − 0.001y2 − 0.007xy is a model for the populations of two species. (a) Does the model describe cooperation, or competition, or a predator-prey relationship? competition cooperation predator-prey relationship (b) Find the equilibrium solutions. (Enter solutions from smallest to largest value of x. If solutions have the same value of x, enter them from smallest to largest y.) (x,y) = (_______) (x,y) = (_______) (x,y) = (_______) (x,y) = (_______)
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- x1'= 5x1-x2+x3 x2'=x1+3x2 x3'=-3x1+2x2+x3 Determine the nature and stability of thecritical point (0,0,0) of system Î. Justify yourconclusion.Draw the phase diagram of the system; list all the equilibrium points; determine the stability of the equilibrium points; and describe the outcome of the system from various initial points. You should consider all four quadrants of the xy-plane. All the following must be included, correct and clearly annotated in your phase diagram: The coordinate axes; all the isoclines; all the equilibrium points; the allowed directions of motion (both vertical and horizontal) in all the regions into which the isoclines divide the xy plane; direction of motion along isoclines, where applicable; examples of allowed trajectories in all regions and examples of trajectories crossing from a region to another, whenever such a crossing is possible.