1. Suppose that y = x³ + 4x. Suppose we increase x from 3 to 3.02. Use differentials to estimate the corresponding increase in the value of y.

Q: 1. Solve the linear differential equation of y' – 2xy = = X. swer:

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Q: The growth of a new restaurant depends on the number of its regular customers as p'(t) = .05√p(t)…

A: TA differential equation is a equation that connects the derivatives of one or more unknown…

Q: 11) Suppose that f is a solution of the differential equation y' + = 1 with f(1) = 1. Then f(2)= 3.…

A: As per the company guidelines We can first question only. Please understand. Kindly repost the…

Q: Consider the differential equation (xy + x)dx = (x²y² – x² + y² – 1) dy. By separation of variables,…

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Q: A population is modeled by the differential equation dP = 1.005P1- dt P 7500 For what value(s) of P…

A: The Given Differential equation is: dPdt = 1.005P1-P7500

Q: Find what m equals given tyll-3kyloMyo the differential equation

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Q: Is the following a homogenous differential equation? dy/dx = (x2y-y2x)/(x3-y3)

A: Let's find

Q: 3. Select the correct type for the following differential equation (10 Puan) (2xy + 3y²) – (2xy +…

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Q: 4. Eliminate the arbitrary constant 'a' in the differential equation: y – 2ay' + x2 = a? %3D

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Q: Straight lines with slope half the value of the x-intercept

A: The equation of a line is defined as y=mx+b, where, m is the slope and b is the y-intercept.

Q: Find general solution for the following linear differential equation: y' + 2ty = 4t.

A: Given that: y'+2ty=4t

Q: What is the general solution of the differential equation of (z + y?) dr + rydy = 0 (22

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Q: 5. Find the differential equation of the family of straight lines with slope 1. с. у-1-0 d. y' +1=0…

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Q: Suppose that in a certain company, the relationship between the price per unit p of its product and…

A: Given,  In a certain company, the relationship between the price per unit P and the weekly sale y,…

Q: Find the Differential Equation of the following family of curves 4. Straight lines with slope half…

A: The equation of straing line is given byy=mx+cwhere,m=slope=dydxand, c=y-interceptat…

Q: The Pacific halibut fishery has been modeled by the differential equation dt where y(t) Is the…

A: the solution of equation y(t) = M/(1+Ae-kt) where A = (M - y(0))/y(0)            A = (9 * 107 -…

Q: Is x = 0 an ordinary point of the differential equation y″+5xy′+√xy=0 ?

A: We have to check

Q: For what values of r does the function y= e™* satisfy the differential equation y"- 4y'+ 2y = 0?

A: for the homogeneous differential equation, the auxiliary equation is  compare this equation with…

Q: Suppose that in a certain company, the relationship between the price per unit p of its product and…

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Q: 5. Find the differential equation of the family of straight lines with slope 1. с. у -130 d. y' +1=0…

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Q: Suppose we know that the graph to the right is the graph of the right-hand side f(y) of the…

A: According to the given information, it is required to draw the rough sketch of the slope field of…

Q: 2x-y? xy? 3- ()dr – ()dy = 0 is exact differential equation. True False o o

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Q: Verify for a > 0, that y = is a solution of the nonlinear differential equation yyll = x.

A: The function is a rule that associates or fixes a number to the particular point x. If , then the…

Q: Find the differential equation of the following families of curves: y2(b+x)=x2(3b-x)

A: Given y2(b+x) = x2(3b-x)                 (1) Differentiate equation (1) with respect to x , we get…

Q: Find the differential equation of the family of -2x y = A1eª + A, e 2a

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Q: Suppose you have the differential equation: y' + p(x)y ln(y) = q(x)y. Prove that the substitution v…

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Q: The following differential equation satisfies the following initial condition y(0)=-3. ydy-xdx-0…

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Q: 3x =2 when x= What is the particular solution to the given differential equa

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Q: The rate of growth of a plant is proportional to the difference between its height h and the maximum…

A: The given data is: The rate of growth of a plant is proportional to the difference between its…

Q: 1. Obtain the differential equation associated with y=Ax2+Bx+C

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Q: Suppose that in a certain company, the relationship between the price per unit p of its product and…

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Q: 2. What should be A for the exact differential equation of ry + A , 2Ay – 1 dr+ y? Moreover evaluate…

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Q: Verify that y(t) = ceat solves the differential equation for unlimited growth, y' = ay, with initial…

A: Given Differential Equation : y1 = ay , y(0) = C i.e. dydt =ayie  dyy = adt Integratinh both side we…

Q: 3. Select the correct type for the following differential equation (2xy + 3y²) – (2xy + x²)y' = 0

A: The given differential equation is: (2xy+3y2)-(2xy+x2)y'=0(2xy+3y2)dx-(2xy+x2)dy=0Here, M=2xy+3y2 ;…

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: The ordinary differential equation 2xy" + y = ycosx is linear False O True

A: Given differential equation is 2xy'' + y = ycos(x)

Q: 8. The complementary function (YCF) when solving the differential equation dy + n'y = 3ksin(pt),…

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Q: Suppose that fit) is a solution of the differential equation y' = ty -2 and the graph of ft) passes…

A: Slope of f(t) at any point will be same at value of y' at that point. Here finding f is not…

Q: Suppose that in a certain company, the relationship between the price per unit p of its product and…

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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: In tracking the propagation of a disease, a population can be divided into 3 groups: the portion…

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Q: From the differential equation dy = x2 dx, what is the equation of y in terms of x as the curve…

A: Given: dy=x2dx

Q: NUTES -3x PG. 8 Problem q: y" =94iyse",y2s e3*

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Q: Let y' – 35y = 7x*e5x. Is this differential equation pure-time, autonomous, or nonautonomous?

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Q: 4. x" +x=e+!.

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Q: 4. Verify that the function y = is an (4 – 12) explicit solution of the differential equation y' =…

A: To veryfy that the function y=14-x2 is an explict solution of the differential equation, y'=2xy2.

Q: Verify that y = (x³ – x) In cx satisfies the differential equation (x³ – x)y' – (3x² – 1)y = x5 –…

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Q: The amount of a radioactive substance, y, decays exponentially such that its half-life is 8 days. In…

A: topic- differential equations

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: 4. Obtain the Differential Equation from the family of curves of the form y = xC

A: To form a differential equation from given family of curves. Differentiate given family of curves…