A circuit consists of a resistor of resistance R and a capacitor of capacitance C, connected in series, and is dv + v= E where E is the constant e.m.f. and v is the dt described by the first order differential equation RC- voltage across the capacitor. Given that v(0) = 0, show by using Linear differential equation method that -t v = E1-e RC

Q: Show that if P(x) #0 the differential equation y' + p(x)y = f(x) is not exact differential equation.…

A: y' + p(x)y = f(x) can be written in the appropriate form dydx + p(x)y = f(x)  ⇒dy +p(x)y dx = f(x)…

Q: Give the order of the given ordinary differential equation and state the type linear or nonlinear (1…

A: Solve the following, note- your options for the degree must include 1. Because a degree of a…

Q: The wall (thickness L) of a furnace, with inside temperature 800° C, is comprised of brick material…

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Q: Suppose that a large mixing tank initially holds 1200 L of water in which 25 kg of salt have been…

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Q: dN = N(1 – 0.0005N) dt

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Q: The Bernoulli equation is a differential equation of the form y'(x) = p(x)y(x) + q(x)[y(x)]",n± 0,…

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Q: A diabetic patient receives insulin at constant rate from an implanted insulin pump. Insulin has…

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Q: Consider the ordinary differential equation dt -x for the range t = 0 to t = a with the initial…

A: Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: Assume that in the absence of immigration and emigration, the growth of a country's population P(t)…

A: In the absence of immigration and emigration the growth rate of the country is given by dP/dt = kP…

Q: Suppose that the population P(t) of a country satisfies the differential equation dt = kP(1200 - P)…

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Q: A circuit consists of a resistor of resistance R and a capacitor of capacitance C, connected in…

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Q: Consider the differential equation y"+ya+x. If g(x) is a solution of the differential equation…

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Q: On the early detection period of COVID-19, there were 557 people verified to have been infected by…

A: 557 people were infected The initial period is Jan 22,2020 dN=(37602-1002.42t+14.6982t2-0.0204t3) dt…

Q: A heart pacemaker consists of a switch, a battery of constant voltage Eo, a capacitor with constant…

A: Explanation  we have given the voltage change E across the heart satisfies the linear differential…

Q: Elimination of ethanol from the blood is known to have zeroth order kinetics. Provided no more…

A: Given data: The given differential equation is dM/dt=-k0. The given value of k0=0.186 g/litre/hr.…

Q: In a city of a fixed population of "P" people , the rate of change (with respect to timet) of the…

A: Given Data: A city has a fixed population is P. Also given, the rate of change (with respect to…

Q: Obtain the differential equation associated with the given primitive, A, B and C being arbitrary…

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Q: Consider the differential equation y' = 1/y - y Find its critical values, and classify them as…

A: Given,y'=1y-yCritical values:1y-y=0y2=1y=±1fy=1y-y∂f∂yy=±1=-1-1=-2<0So, both y=-1 , -1 are…

Q: The differential equation governing the free response of an accelerometer is given as: 4.6 x 10-12 i…

A: Given differential equation, 4.6×10-12x¨+5×10-7x˙+0.4=0 Lets write given equation in second order…

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Q: A model of a spring/mass system is 4x" + e0.1x- 0. By inspection of the differential equation only,…

A: Given - A model of a spring/mass system is 4x'' + e-0.1tx = 0. To find - By inspection of the…

Q: A mass of 50 kg is attached to a spring whose constant is 32 N/m

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Q: For a second order linear homogeneous ordinary differential equation with constant coeffi- cients,…

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Q: Suppose that a large mixing tank initially holds 300 gallons of water in which 50 pounds of salt…

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Q: An electric circuit, consisting of a capacitor, resistor, and an electromotive force can be modeled…

A: Please see below pictures for detailed solution.

Q: Consider the second-order differential equation for y (т — 1)}"(х) — ху (г) + у(х) — 0 -- of which a…

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Q: Suppose that a large mixing tank initially holds 900 gallons of water in which 50 pounds of salt…

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Q: The study of undamped oscillations under the influence of an external force F(t) =F0 cos(ωt) leads…

A: Solution:

Q: The differential equation governing the velocity of an object is dv = -kv", dt where k > 0 and n are…

A: The given differential equation is dvdt=-kvn, where k>0 and n are constants and v(0)=v∘. At t=0,…

Q: y" -y'-zy= 4et

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Q: Suppose that a certain population has a growth rate that varies with time and that this population…

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Q: The linear and homogeneous differential equation of order 2 with coefficients in the range (a, b) is…

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Q: A certain virus is known to spread among a population at a rate proportional to the fraction of the…

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Q: Consider the differential equation (DE) given by y" + 2y' + 2y = 2e¬2= + 2x. (a) Determine i) the…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Suppose y1 and y2 form a fundamental solution set for the differential equation y" + P(x)y' + Q(x)y…

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Q: Suppose that a fourth order differential equation has a solutiony Sc sn(r) a) Find such a…

A: The auxiliary equation of the differential equation with solution y=8e4xxsinx is : m-4-i2 m-4+i2=0

Q: Solve the first-order differential equation dydt=ay with the initial condition y(0)=5 Specify the…

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Q: A heart pacemaker consists of a switch, a battery of constant voltage Eo, a capacitor with constant…

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Q: At a time denoted as t = 0 a technological innovation is introduced into a community that has a…

A: Given information: Given that at a time denoted as t = 0 a technological innovation is introduced…

Q: Suppose that a large mixing tank initially holds 300 gallons of water in which 50 pounds of salt…

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Q: Suppose that a large mixing tank initially holds 700 gallons of water in which 50 pounds of salt…

A: Given: A tank containing 700 gallons of water in which 50 pounds of salt is dissolved. Rate at which…

Q: A diabetic patient receives insulin at constant rate from an implanted insulin pump. Insulin has…

A: Consider a first order differential equation isdMdt=a-k1M, where a>0,k1 is the fraction of…

Q: Suppose that the population Pt) of a country satisfies the differential equation P(400 - P) with k…

A: It is given that population P(t) satisfies the differential equation-…

Q: An annuity is a fund into which one makes equal payments at regular intervals. If the fund earns…

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Q: 2. A differential equation that is a function of x only O will produce a slope field with parallel…

A: Here, given that the differential equation is a function of x only. So, dydx=f(x)⇒y=F(x)+C, where…

Q: Suppose that a fourth order differential equation has a solution y=−8e5xx cos(x). Find the initial…

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Q: A pond initially contains 8,000,000 gal of water and an unknown amount of an undesirable chemical.…

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Q: A farmer selected a variety of a fast-growing vegetable which matures based on the differential…

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Q: Consider the differential equation (DE) given by y" + 2y + 2y = 2e¯2= + 2x. %3D (a) Determine i) the…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.