Find a formula for f(n)(x) if f(x) = e' -3x fln)(x):

Q: Find the Differential equation by eliminating the arbitrary constant y= A + bex

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Q: Find the differential equation corresponding to y=a cos (logx) +b sin(logx) or y=A sin (logx)…

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Q: Find the differential equation by eliminating the arbitrary constant y= A + bex

A: Solution:-

Q: Solve the equation difFerential Ci+ x) y' + y = Jx %3D

A: Given differential equation is,

Q: An integrating factor for the differential dy + my = e-m² is dx equation

A: Given differential equation is dydx + my = e-mx

Q: Find the differential equation of straight lines with slope and x –intercept equal.

A: Recall:  The equation of straight line is y=mx+b where, m=slope, b=y-intecept   Given, slope and x…

Q: 1. Differentiate the implicit equation with respect to x. x³ + y³ ln(x) + e²y = 4

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Q: y' + 2xy = 0

A: y'+2xy=0

Q: If N(x) = sin x – sin θ and D(x) = x – θ, find the limit of N(x)/D(x) as x approaches θ. (SOLVE BY…

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Q: In y = C₁e* + C₂е¯x

A: Given problem:- Find its differential equation through eliminating arbitrary constants.    In(y) =…

Q: Obtain the differential equation by eliminating all arbitrary constants

A: We need to eliminate constant B.

Q: Determine whether the differential equation -dx = e* is x' +1 separable or not. If yes, solve it.

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Q: Find the particular solution that satisfies the differential equation and the initial condition.…

A: f(x)=∫f'(x) dxf(x)=∫(16x3-6x)dxf(x)=16x44-6x22+C              (∫xndx=xn+1n+1)f(x)=4x4-3x2+C where…

Q: Solve the differential equation by variation of parameteres: y'' + y = sec(x) + tan(x)

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

A: dA/dt=kA

Q: he population y(t) of a certain microorganism grows continuously and follows an expo uadrupling time…

A: In this question, the concept of derivatives is applied. Derivative We can use a derivative to…

Q: Solve the differential equati on. dz (log x) = –(log z) dx X

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Q: Use integration to find a general solution of the differential equation                  dy / dx =…

A: The given equation is  dy / dx = tan2 x

Q: Find the differential equation by eliminating the arbitrary constant/s. y = = Aex cos x + Bex sin.x…

A: We differentiate the number times as the number of arbitrary constants present in the equation and…

Q: Solve the differential equation by variation of parameters. у" + у %3 csc х y(x)

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Q: Obtain the differential equation associated with the given non-derivative equation in x and y. Show…

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Q: Is the differential equation x" + e^x - 1 = 0 conservative or non-conservative? Explain why? If it…

A: Given x''+ex-1=0

Q: ① Solveing dy - - x dx = 。 ㅎ

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Q: f f(x) = ex – e-x – 2x and g(x) = x – sinx, evaluate the limit of f(x)/g(x) as x approaches zero.…

A: Here we have, f(x)=ex-e-x-2x and g(x)=x-sinx We have to evaluate limx→0f(x)g(x)=?

Q: 1. x In x sec² y dy + [tan y – (In x)°]dx = 0 When:x = 1; y = "

A: The given differential equation is solved below in detail.

Q: Use integration to find a general solution of the differential equation

A: Given: dydx = xex2  To find: General solution of the given differential equation.

Q: Find the differential equation of the family of cissoids: y^2 = x^3/ (a-x)

A: Perform the differentiation and eliminate the constant term in the differential equation to obtain…

Q: Determine whether the statement "The function y = 0 is always a solution of a differential equation…

A: Here the given statement is The function y=0 is always a solution of a differential…

Q: verify that the indicated function is an explicit solution of the given differential equation…

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Q: Assume that the rate of evaporation for water is proportional to the initial amount of water in a…

A: Here, given that rate of change of evaporation is proportional to the initial amount of water.…

Q: 15. x" + x = tan t; x=-(cost) In(sect + tant)

A: Given, x''+x=tant x=-costlnsec(t)+tan(t)x''=cos(t) ln(tan(t)+sec(t))+tan(t)

Q: Find the particular solution that satisfies the differential equation and the initial condition.…

A: Given that f'(x) = 20x3 - 8x and f(1) = 1 then find particular solution. Here i attached solution of…

Q: Obtain the differential equation associated with the given non-derivative equation in x and y. y =…

A: Given that obtain the differential equation associated with the given non-derivative equation in x…

Q: Solve the differential equation by variation of parameters. ✓+y=sin²(x) - con(x) + cylin(x) + con(x)…

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Q: Solve the differential equation by variation of parameters. y" + y = csc(x) y(x) = c₁cos(x) +…

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Q: Find the particular solution that satisfies the differential equation and initial condition. x2…

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Q: what is the differential coefficient of x.

A: To find differential coefficient of x we need to differentiate x with respect to x.

Q: By first finding an integrating factor, solve this differential equation. Give your answer in the…

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Q: Find the differential equation using elimination of arbitrary constants

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Q: What differential equation has y = x² cos y - 4x + C as a solution?

A: We have to find

Q: 3 +Ve³ .2 3x e: f(x) =

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Q: The differential equation governing the decay of a certain radioactive substance through time is dq…

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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: The differential equation governing the decay of a certain radioactive substance through time is dq…

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Q: 6. A certain radioactive material has a half-life of 100 days. If the amount of material present, x,…

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Q: Find the particular solution that satisfies the differential equation and initial condition. f"(x) x…

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

Q: Find a special solution of yn+2 - Yn= fo = constant by variation of parameters.

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