y'+ytan(x)=cos^2(x) ,      y(0)=-1

Q: Use a computer algebra system to graph the slope field for the differential equation and graph the…

A: Given Data The integral is ꭍ03 xex²dx.   Let,

Q: dx dy dz y +z X + y X +2

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Q: Solve the partial differential differential by separation of variables 70z + 6 = 0.

A:

Q: The number of internet users in a country increases at a rate that is jointly proportional to the…

A: Let number of people having personal computer be C(constant), number of people having internet be N.…

Q: determine the general solution to thegiven differential equation. Derive your trial solution…

A:

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: 9. From the differential equation sinh 2x, sketch some of the family of curves. %3D dx

A: Given differential equation, dydx=sinh(2x)dydx=e2x-e-2x2∫dy=∫e2x-e-2x2dxy=e2x+e-2x4+C

Q: Please explain the general process( steps taken)  for solving any nonhomogeneous linear differential…

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Q: (3nny-5x)dx+ 2x*cotydy = 0

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Q: Explain when Euler’s Method produces an exact particular solution of a differential equation?

A: Euler’s Method produces an exact particular solution of a differential equation?

Q: What is a separable differential equation? How do yousolve it?

A: In a separable differential equation, we separate the variables and then take the integration of…

Q: y using an integrating factor, find the general solution of the differential equation dy/dx…

A: Given differential equation :                          dydx-ytanx=sinx

Q: solve the differential equation for initial value problem using the method of undetermined…

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Q: Explain the steps to determine the a single particular solution of anonhomogene linear differential…

A: Consider a second order non-homogeneous linear differential equation with constant coefficients,…

Q: %3D siny(x + siny)dx + 2x²cosydy = 0

A:

Q: Find general solutions of the differential equation    (2xsinycosy)y'=4x^2+sin^2 y

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Q: Obtain the differential equation by eliminating all arbitrary constant.

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Q: Find the differential equation of the family of curve Straight lines with slope half the value of…

A: solutionGivenstraight line y=mx+CAlso givenslope =m=dydxC= y interceptat x intercept, y=0Also given…

Q: From the differential equation by elimaniting arbitary constant y =ax'+ bx²

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Q: solve for exact Differential Equation (ex + ln y + y/x)dx + (x/y +ln x + sin y)dy = 0

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Q: Assume that a population P of wolves in a region is proportional to the area A of the region. Does…

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Q: From the differential equation by elimaniting arbitary constant  y=ax3+bx2

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Q: A 2-lb object, that stretches a spring by 1.5 inches, is released with a downward velocity of 32…

A:

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

A: Equation of straight line: y=mx+c Where, m = slope  c = y-intercept

Q: y In(x) ln(y)dx + dy

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Q: Use a technique of integration or a substitution to find an explicit solution of the given…

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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: A: By using Linear equation solve the first order differential еquation y' + sec(x)y = cos(x)

A: The given differential equation is;  y'+sec(x)y=cos(x).

Q: al csc x y cotx

A: We have to find the intregating factor of given differential equation.

Q: Obtain the differential equation of the family of straight lines passing through (0,-1).

A: To Obtain the differential equation of the family of straight lines passing through (0,-1).

Q: 3. ydx+(1+x)arctanx dy= 0

A:

Q: A 2-lb object, that stretches a spring by 1.5 inches, is released with a downward velocity of 32…

A: Given:    mg = 2    s = 1.5 inches = 1.5/12 = 1/8 feet     g = 32

Q: dy COS X + y sin x = sec² x dx solution of above differential equation is

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Q: Find general solution of differential equation. Enter transient terms if any. x^2y' + xy= 7

A: Here we will find out the required general solution for given differential equation.

Q: In a city of a fixed population of " people , the rate of change (with respect to time t) of the…

A: Given Data: A city has a fixed population is P. Also given, the rate of change (with respect to time…

Q: If the family of curve has 3 arbitrary constants then the corresponding differential equation is

A:

Q: A normal is drawn at a point P (x, y) of a curve, it meets the x-axis at Q. If PQ is of constant…

A: We will show that the given differential equation describing such curve is correct and will find the…

Q: . Give an example of a nonlinear differential equation of the formy = f (y).

A: Solution: Nonlinear Differential Equation: A nonlinear differential equation is a differential…

Q: Find the differential equation using elimination of arbitrary constants

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Q: The capacity of the theater is 500 people. At a certain time, the number of people in the theater is…

A: The capacity of the theater is 500 people. At a certain time, the number of people in the theater is…

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

A:

Q: Describe the separation-of-variables technique for obtainingthe solution to a differential equation.

A: To describe the separation of variable technique.

Q: A/ By using Linear equation solve the first order differential uation y' + sec(x)y= cos(x)

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Q: What is the differential equation of family of parabolas with vertex on the x – axis and axis…

A: General equation of parabola parallel to y-axis and having center (h, k) and having distance 'a'…

Q: 3. (sin'x + cosv)dx - tanxsin2ydy = 0

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Q: Suppose that a large mixing tank initially holds 300 gallons of water in which 50 pounds of salt…

A: Given, Initially, the tank holds 300 gallons of water in which 50 pounds of salt have been…

Q: SOLVE FOR THE DIFFERENTIAL EQUATION OF THE GIVEN FAMILY OF CURVES. 1. Parabolas with vertex and…

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Q: If an object's mass is changing at a rate proportional to its weight at a given time, does it make…

A: Two quantities are said to be proportional if they are increase or decrease in same manner. In such…

Q: Calculate the truncation error to solve the differential equation: Yi+1¬Yi = Xị → (*) Ax dy Instead…

A: Follow the following solutions to get the complete correct answer.

Q: azu Ex: Solve the partial differential equation дудх sin³x cos²y given that du %3D siny when x=0 and…

A: First take x as a constant and integrate with respect to y and the other one

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.