Solve the following initial value problem. y - y = )e^dA, y(0) = -1. %3D |

Q: 7. A 170kV 3 phase electric source delivers 200 MVA to a balanced load with pf of 90% lagging. What…

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Q: A breeder reactor converts relatively stable uranium 238 into the isotope plu- tonium 239. After 15…

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Q: A certain radioactive material is known to decay at a rate proportional to the amount present. If…

A: given,     radioactive material is decay at a rate proportional to the amount present .initially 50…

Q: find the timear form of this differential equation

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Q: Consider a pond with 10000m3 of clean water that has water feeding into it from Stream A and water…

A: Given- Consider a pond with 10000m3 of clean water that has water feeding into it from Stream A and…

Q: 2. The rate of decay of radium is proportional to the amount present at any time. If 60 mg of radium…

A: A(t) = amount remaining in t years          = A0ekt, where A0 is the initial amount and k is a…

Q: Find the general solution of the differential equation for interest compounded continuously,dA/dt =…

A: dA/dt=kA

Q: Explain briefly the classifications of the Differential Equations?

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Q: A murder of crows in the wild is observed to double its population in one year. However, in…

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Q: Write the differential equation satisfied by y = Cekt.

A: Given equation is              y=Cekt

Q: Suppose that glucose enters the bloodstream at the constant rate of r grams per minute while it is…

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Q: Suppose that a population has a rate of growth of 0.1 and a carrying ranacity of 2 million, Şet up…

A: The population dynamics can be modeled through a first-order differential equation. It contains the…

Q: When air expands adiabatically (without gaining or losing heat), its pressure P C where C is a…

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Q: Find a differential equation whose general solution is y = cie®t + cze¬,

A: The complimentary function of the differential equation if the root of the auxiliary equation are…

Q: The population of a community is growing at 2% per year and its per capita consumption is growing at…

A: Given that: Population growing rate of a community is 2% per year Per capita consumption growth rate…

Q: The population of Japan in 1960 was 94 million, the population in 1970 was 105 million. Set up and…

A: Given that the initial population of Japan in 1960 is 94million and the population of Japan in 1970…

Q: Please solve the initial value problem and show your work clearly. Thank you.

A: Introduction: Calculus is a branch of mathematics that focuses on rates of change, differential…

Q: 2. The radioactive isotope of lead, Pb-209, decays at a rate proportional to the amount present at…

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Q: If the number of fruit flies F increases at a rate that is proportional to the number of flies…

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Q: Give two examples of your own for order and degree of a differential equation

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Q: Solve the initial value problem y′+ysinx=sinx and y(π/2)=1

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Q: A population of wild horses is represented by the logistic differential equation dP/dt =…

A: Given: The logistic differential equation is, dpdt=0.08p-0.00004p2          (1) To find: A) The…

Q: A storage battery discharge at a rate which is proportional to the charge. If the charger is reduced…

A: Solve by making equation

Q: Solve for when the population increases the fastest in the threshold logistic equation : 1000 P'(t)…

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Q: Show your working while calculating the instantaneous rate of increase (dN/dt) at 4 K and ¼K. Is it…

A: question:

Q: A zircon sample contains 4000 atoms of the radioactive element 235U. Given that 235U has a half‐life…

A: Given- A zircon sample contains 4000 atoms of the radioactive element 235U and 235U has a half‐life…

Q: The rate at which radioactive nuclei decays is proportional to the number of such nuclei that are…

A: Given Half of the original number of radioactivenuclei have undergone disintegration in a period of…

Q: How can you tell that a differential equation is separable? Thatit is linear?

A: We can say differential equation separable  if it  can be written so that all terms in x and all…

Q: Find the general solution of the differential equation with clear steps.

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Q: Find the linear, nonhomogeneous differential equation with constant coefficients whose solution is y…

A: We have to find homogeneous differential equation first.

Q: A breeder reactor converts relatively stable uranium-238 into the isotope plutonium-239. After 15…

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Q: 19.) [(ycoth y² )log°(sinh y² )dy

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Q: The amount of radio active material present at time t is given by A=Aoe*t, where Ao is the initial…

A: As many Questions are given , I will solve only one: Let A0 be the initial amount. Given that a…

Q: у" + 16у — 0; Уi — сos 4x

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Q: When time is measured in days, the decay constant for a particular radioactive isotope is 0.14.…

A: The decay of an object follows the exponential model  where N(t)I is the amount remaining after time…

Q: A breeder reactor converts relatively stable Uranium 238 into the isotope Plutonium 239. After 15…

A:

Q: The decay equation for radon-222 gas is known to be y = y0 e-0.18t, with t in days. About how long…

A: The decay equation for radon-222 gas is known to be y = y0 e-0.18t, with t in days. About how long…

Q: The total number of reported cases of an illness in a large city days after the start of an outbreak…

A: According to the given information the total number of reported cases of an illness in a large city…

Q: A man is walking at a rate of 1.5 m/s toward a street light which is 5 m above the level ground. At…

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Q: From the differential equation by elimanating arbitary constants  y=ax3+bx2

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Q: A radioactive isotope decays at a rate proportional to the amount of the isotope, in other words…

A: Given,  k = -0.283033 , let initial amount = C= 1 , final amount =A=0.5  We have to find t

Q: Use separation of variables to find the general solution of the differential equation. ely' = 3x5 +…

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Q: If a bus travelling at 25 m/s is subjected to a steady deceleration of 5 m/s?, how long will it take…

A: If a bus travelling at 25 m/s is subjected to a steady deceleration of 5 m/s2 .We have to find  how…

Q: Solve for when the population increases the fastest in the threshold logistic equation : 1000 P'(t)…

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Q: What is the degree of the differential equation:

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Q: A radioactive material decays continuously at a rate proportional to the amount present. After 2…

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Q: Show that solving the logistic differential equation results in the logistic growth function

A: The given differential equation is dydt=825y54-y   with  y0=1. Solve the above differential equation…

Q: 8. Determine the half-life of the substance if an initial 150mg has decayed to 50mg in a an of 20…

A: Given query is to find half life and the time when 95% amount decayed.

Q: The half-life of plutonium 239 is 24,200 years. Assume that the decay rate is proportional to the…

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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.