1. Given that A(x) = | t² – t dt, find the following. (a) A(1) = (c) A'(3) = (b) A'(1) = (d) A(x) =

Q: Find the differential dy of the given function. y = csc 2x

A: Consider the function

Q: Find the differential dy of the given function.

A: Given :              The given function is :                   y = 9 - x2 To find :            The…

Q: Given the function y = x3 + x² + x + 10, suppose x increases from 1 to 1.1. Find the absolute error…

A: We will find out the required value of absolute and percentage error.

Q: Find the differential dy of the given function.

A: Here we will Compute the first derivative dydx  And the rule we will use for computing is known as…

Q: y' – y = 2te',

A: Laplace transform: L(y'(t))=py(p)-y(0) L(y(t))=y(p) L(2tet)=2(p-1)2

Q: dy ay +b whose dt Write down a differential equation of the form all other solutions diverge from y…

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Q: Find the differential equations for each family of curves under the following conditions: c)…

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Q: Solve the differential equatons x(2y + In ax) dy + (x+y)dx when x=3 y=Ź y= 2 1.

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Q: z = x siny + y sinx

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Q: Write down a differential equation of the form =ay + b whose dy dt solutions all approach y = 6 as…

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Q: 6. Write down the differential, dy, of y = e3x.

A: to find the differential of y=e3x

Q: Solve the following differential eyuation x 2+ 2y = x* e** y.

A:

Q: Find the general solution of the differential equation with the help of lablace transform

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Q: What is the differential equation obtained by eliminating the parameter A from the relation y = A +…

A: Here we find the first order differential equation of given function.

Q: 3. Write the exact differential: f(x,y)=e-y-el-

A: Given- fx,y=ex-y-ey-x To write the exact differential.

Q: Find the differential dy of the given function. y = InV9 - x2 dy =

A:

Q: Write the corresponding differential equation in time domain. F(s) X(s) s³ + 11s² + 12s + 18 s+3…

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Q: 4. u = xz siny + yz cosx + xy tanz

A: Given,  u=xz sin y+yz cos x+xy tan z

Q: 5. Verify that y(x) = Vx+C is a solution of the differential dy dx 1 for every constant C. equation…

A: The differential equation is given as dydx=12y2ydy=1dx

Q: Find the differential dy of the given function. y = (x + 1)/(2x − 1)

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Q: Eliminate the arbitrary constants (a, b) in the function to obtain the differentialequation. e* =…

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Q: Show that cos x is the integrating factor of the linear differential equation dy/dx= sec x+y tan x

A: Integrating factors are useful for solving ordinary differential equation  that can be expressed in…

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

A: First rearrange terms in the given ordinary differential equation  dyy=0.5+sint5dt since it is…

Q: If y approximate the differential dy when x changes from 64 to 64.07

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Q: Jesaki Inc will sell N units of product after spending $x thousand in advertising, as given by N =…

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Q: Find the lower bound for the radius of convergence for the following differential equation: (x^2 +…

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Q: S(«,9) =7+3y Also, find the total differential of the function.

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Q: What is the differential equation of the orthogonal trajectories of the family of curves y = Cx ? (A…

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Q: Find the differential dy of the given function. y = √√√√9-x²

A: Given y=9-x2 we need to find dy

Q: х+1 y 2x 1

A: Given,            y = x + 12x - 1

Q: Derive a differential equation for the orthogonal trajectories of the family  of curves xy=c

A:

Q: Write down a differential equation of the form = ay + b whose ay dt all other solutions diverge from…

A: We have to determine a differential equation of the form dydt=ay+b. The solution of differential…

Q: The differential equation for cooling of a cup of coffee is given by dT dt = -(T – Tenu)/T where T…

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

Q: Obtain the differential equation of the family of straight lines with slope and y-intercept equal.…

A: Differential equations

Q: 2. If y = find the differential dy. Hence, estimate the value of 1 + (1.023 1 +

A: topic- differentials

Q: 1. Construct a slope field for the differential equation = dy x + 2y dx

A: The given differential equation is: dydx=x+2y So the slope at any point (xo,yo) will be given by…

Q: 8. Compute the differential df of f(x,y) = log (x² + y²).

A: Given; f(x,y) = log(x2+ y2)

Q: The integrating factor that transform the differential equation y" +y' + Axy = 0 into a…

A: Given - The differential equation y'' + 1xy' + λxy = 0 To find - The integrating factor that…

Q: Consider a differential equaUion -x2 y' = xy + xe

A: we have been given a differential equation with initial condition y(0)=0 y'=xy+xe-x2

Q: Without solving explicitly, classify the critical points of the autonomous differential equation dx…

A: See the solution and follow the steps. You will understand easily.

Q: There is considerable evidence to support the theory that for some species there is a minimum…

A: Given: dPdt =-rP1-PK1-PT  , P ,t≥0r=0.01 , K=13000 , T= 400 To check where population increases and…

Q: Jesaki Inc will sellN units of product after spending $a thousand in advertising, as given by N = 73…

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Q: Consider the nonhomogeneous differential equa 1 "(x) + y(x) = e '+ sin a

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Q: Determine the differential equation of the family of lines passing through the origin O ædx + ydy =…

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Q: The dynamics of a fish population is described by the Richard's growth law dN (1) dt where N = N(t)…

A: rN is the part of the equation which signifies the rate of change of population dN/dt. r is the…

Q: Find the function ?(?) that satisfies the differential equation dy/dt - 2ty = -6t2et^2 and the…

A:

Q: (1/4) Estimate the value of 82 a. approximation b. differentials

A: To estimate the value of 8214 by using a approximationb differentials

Q: If y = 5x2 + 2x + 9 , find the value of the differential dy as x changes from 3 to 3.1

A: Given, y = 5x2 + 2x + 9Differentiating with respect to x;dydx = 10x + 2At x = 3, dydxx = 3 = 10×3 +…

Q: Find the differential equation of the family of curves y = mx + b where m = b.*

A: We have to solve given problem: