The equation of motion of a train is given bydvmk (1-e")-.m%3D- mcvdtwhere v is the speed, t is the time and m, k and c are constants.(a)Show that vet = kecte'(c-1)+z by using Linear Differential Method.с -1

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Answered: The equation of motion of a train is…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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stanit 7 Write a differential equation of the form dy = f(x, y) that has y = g(x) as a solution, where the graph of y = g(x) is normal to every curve of the form y = x² + k (k is a constant) where they meet. Write a differential equation that is a mathematical model of the situation described.
The tank contains 3 kg of dissolved saltbe up to 75 liters of water. Saline solution of strength0.4 kg of salt / L is pumped into the tank at speed6 L / min.• Solution is drained from the tank at the same speed.• Set up a differential equation that describes this system.Let's solve the differential equation and get a function thatdescribes the salt content of the tank at time t.
A 160 pound object is suspended from a spring The spring stretches an extra 80 inches with the weight attached. The spring-and-mass system is then submerged in a viscous fluid that exerts 18 pounds of force when the mass has velocity 2 fisec. What is the differential equation for this spring-and-mass system? (Use u as the dependent varlable) This system is? For what value of y would the system be critically damped? (if the given system is already critically damped, enter the given value for y)
Which differential equation is variable separable? (A) xy dx + (x² + 1) dy=0 (в) (х2+ у) dx - Зху dy%3D0 B (e* + y) dx + sinx cosy dy=0 (D х2 dx + (3x- у) dy %3D0
Consider the differential equation: dy/dx = y(3 - y) 1) Use the slope field plotter to plot different solutions corresponding to A: (0,-2); B: (0,1); C: (0,3); D: (0,4). You can drag each point to the correct place if they're somewhere else on the plane, or click on the point and redefine. Capture a screenshot showing all the solution curves and insert below. f'(x)=y(3-y) Kin/5 -5 Density Length dy de -8 Step size 0.1 Ymas y (3-9) Input. ✔Solution A Solution B Solution C Solution D DCQ= AC: 2) To what value does y(x) approach, as x → ∞, for the solutions corresponding to B,C, and D? To what value does y(x) approach, as x →∞, for the solution corresponding to A? Why is it different from the others? Be specific and answer in terms of what you know about the slope field and its effect on the solution. - 3) Use wolframalpha.com or something similar to find the particular solution corresponding to each of the points A,B,C,D. How is the solution through Point C different from the other…
Which of the following systems of differential equations would dictate the rates of change of the salt concentration for the two-tank system shown below? 10 L/min 70 g/L VAL 14 L/min I 6 L/min OC A/= (1/VA) (10 × 70 + 6cg - 14CA), c_l= (1/V₂) (14c. – 16c) OC Al= (1/VA) (70 – 6cв - 14CA), CB= (1/VB) (14CA - 16CB) 16св) VB L C Al= (1/VA) (14CA CB/= (1/VB) (14CA - 16CB) 10 × 70 – 6cß), C Al= (1/VA) (10 × 70+ 16cB - 14CA), CB/= (1/VB) (14CA 10CB) 10 L/min
please do d)
azu Ex: Solve the partial differential equation дудх ди sin³x cos?y given that siny when x=0 and u=2 when ду %3D y=0

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The equation of motion of a train is given by dv mk (1-e")-mcv dt m %3D where v is the speed, t is the time and m, k and c are constants. I eet e(c-1) (a) Show that ve = k +z by using Linear Differential Method. C с -1