A given scenario of a person falling into a pit attached to a rope can be modeled by the second-order non-homogeneous differential equation mh'' + 5h' + 120h = mg where m is mass of person and g is gravity. This equation can be converted into a system of first-order differential equations with initial conditions h(0) = 100 and v(0) = 0. How does the solution of this system vary for different masses m? In other words, how will the height h(t) and velocity v(t) change as we increase m?

Q: A tank with a capacity of 250 gal is intended to be used to prepare a sugar solution. The tank…

A: Let the amount of sugar in tank at time t = y(t)

Q: Suppose that the auxiliary equation of a fifth-order homogeneous linear differential equation with…

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A: Your requirement is the particular solution up(t) as specified format.

Q: Suppose that a large mixing tank initially holds 500 gallons of water in which 50 pounds of salt…

A: Thus, we need to find  and  first.Here,         (concentration of salt in inflow).(input rate of…

Q: This is a differential equations problem.

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A: Every system of differential equations can be written in vector form also.

Q: (c) Draw the phase portrait of this system.

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A: given differential equations x1'=9x1+4x2x2'=-6x1-x2x3'=6x1+4x2+3x3 explanation we can write it in…

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Q: 5. An object weighing 8 pounds stretches a spring 4 inches. In addition, the system is inside a…

A: 0.25y"+3y'+24y=0y(0)=0.25 fty'(0)=-1 ft/sExplanation:If you have any doubt please let me know in…