Laboratory department detects the concentration C of impurity of an oil purifier changes with time t and is described by the equation = b+ dm - Cm, where b,d,a and m are dt constants. Given C = Co and when t = 0. Solve the equation and show that -mt c= + a][1- e=]+ co e -mt

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A: Use the logistic differential equation to find out the answers shown below.

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A: Given, d2ydx2-a2y=w2Elx2-lx So, the characteristics equation of the given equation is, m2-a2=0m=±a…

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Q: Use exponential shift to find the general solution of the differential equation. (D+1)°y = 0

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Q: (i) Show that the solution of the logistic equation dr az – br dt (3) is given by 1(t) a – br(t)…

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Q: A constant-stirred tank reactor (CSTR), initially filled with 20 kg of salt, is diluted with enough…

A: dSdt = 180s +40 S = salt concentration = 20kg s = 1% of original amount = 1% of 20 = 0.02kg

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A: final answer is  T = 200 C at t =5 minutes detailed solution with explanation is given below

Q: (D² -1)y= 2(1-e-2*)-1/2

A: By Using  variation of parameter

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Q: Find all solutions to the differential equation. Use c to denote an arbitrary constant. y' = x ln(x)…

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Q: Q4: Find the general solution of the differential equation y'+ (tan x)y = sec2 x %3D

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Q: Let y = Cre". For which values of C is y a solution to the differential equation y" = y+4e#?

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Q: Use variation of parameters to solve the differential equation: -2x y" + 4y' + 4y : In x. = e

A: Here I am attaching image so that you understand each and every step.

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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.