Find the differential equations of the families of curves. 1.) Straight lines with slope and y-intercept equal.

Q: y' – (cotx)y = -(2cosx)y-2

A: Handwriting solution

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Q: a) Form a differential equation from the given function. y = Asin(2x)-5cos(2x)

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Q: Verify that the indicated family of functions is a solution of the given differential equation.…

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Q: (5 points) Find the solution to the differential equation dz 4te? %3| dt that passes through the…

A: We have to separate the variables first.

Q: ne following second-order differential equa

A: Introduction: A second-order differential equation has a form d2ydx2+p(x)dydx+q(x)y=r(x), where…

Q: 4. Which of the following represents the differential equation of the family of parabola having…

A: Follow the procedure given below.

Q: Q1 Prove that the differential equation below

A: Given,         (x-2y)dx+(y-2x)dy=0

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Q: (ii) Show that the differential equation is not exact. (2y² + 3x) dx + 2xydy = 0

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Q: Give the differential equations for the Malthus model and the Verhulst model. Give a graphical…

A: The differential equations for the Malthus model and the Verhulst model. Give a graphical…

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Q: Given the differential equation -(승) (중), y" Find two values of r such that y = x' is a solution of…

A: The given differential equation is y''-6xy'-8x2y=0. Let y=xr. This gives  y'=rxr-1     and…

Q: which one of the following is not a criterion for linearity of an ordinary differential equation? a.…

A: Given that: Conditions for linearity of a differential equation.

Q: construct a first-order linear differential equation whose solutions have the required behavior as t…

A: Given that: The equation of the line y = 2t - 5 as t→∞

Q: The differential equation of the family of straight lines whose sum of slope and x-intercept is…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: 11. Obtain the differential equation of the family of parabolas y =x +c and sketch those members of…

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Q: q22 When monitoring the spread of disease, the population can be divided into three groups; the…

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Q: The following sigmoid graph is used to model the population of vaccinated people in New Zealand…

A: The solution of this question is given below:

Q: Find a differential equation of the following family of curves whose solution is: 1. A family of…

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Q: The differential equation of the family of straight lines whose sum of slope and x-intercept is…

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Q: Write a differential equation that is a mathematical model of the situation described below:…

A: Use the general equation of a line passing through a point and with given slope to determine the…

Q: 2 3. Scanned with CS CamScanner

A: we have obtain the differential equation from the given curve

Q: What is the differential equation of all straight lines? A. y' = 0 В. у" %3D 0 C. y' = 1 D. y' = 0…

A: Differential equation of all straight lines

Q: dy What does the solutions of the differential equation = -7represent ? dx

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Q: Q1. Show that the given function is a solution of the differential equations. y = e-* + sinx y" + y…

A: Given differential equation                                              y''+y=2e-x    or…

Q: 13. What is the degree of the differential equation below? dz 3rd degree 1st degree

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Q: (a) The order of this differential equation is (b) Is the equation linear?

A: Given: d2ydt2+sin(t+y)=sint To find: (a) The order of this differential equation  (b) whether the…

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A: Given: fz=z2y2 To find: Differential equations

Q: paraller ines, the involves transforming the original DE into a homogeneous differential equation.

A: We will use concept of differential equation.

Q: 5. Find the general solution of the differential equation using GeoGebra (D² +9)y=2 sina

A: General equation of differential equation.

Q: Solve the differential equation. regarding y as the independent variable rather than x. by |26. (1 —…

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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: Can a differential equation be both separable and linear? Ex-plain why not, or give an example of an…

A: Can a differential equation be both separable and linear?

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

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Q: Find the Differential Equation of the following family of curves

A: Differential equation formation

Q: Bob starts working at age 20 and his pay is $15,000 a year. Over the next 10 years he receives pay…

A: Let's solve.

Q: decide if the given statement is true or false,and give a brief justification for your answer.If…

A: Given the differential equation                        x2y” + (9x – 2x5)y’ + (25 + 5x2 + 10x4)y = 0…

Q: у %3D у? + 5у + 6

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Q: A differential equation and its slope field are given. Complete the table by determining the slopes…

A: Given that, dydx=tany6

Q: If the characteristic equation (the auxiliary equation) of a higher order linear differential…

A: Handwriting solution

Q: Match the differential equations with their slope fields, graphed Attached. y' = x + y

A: Given: The differential equation y'=x+y To determine: Slope fields of the given differential…

Q: Find the corresponding differential equation for the following family of curves. 1. All Straight…

A: The general equation of the family of straight line is given by y=mx+b, where m and b are arbitrary…

Q: y3D C1e3x + c2e3*

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Q: 3.Find the differential equations for each familyof curves under the following conditions:…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Decide if the differential equations whose slope fields are shown below involve only x, only y, both…

A: The y-axis is for the value of 'theta'.  It can be seen that with a change in theta value the slope…