y" – y' = sin(t) y(0) = 1 y' (0) = -1

Q: SOLVE FOR EXACT DE DIFFERENTIAL EQUATION 3. (x + 3)cos ydx - [siny In(5x + 15) - y] dy = 0

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Q: Find the differential equation (Family of Curves): Strophoids : y2=x2((c-x)/(c+x))

A: If a equation consists of n arbitrary constants then the differential equation of the given relation…

Q: 18. What is the integrating factor of the differential equation y' =cscx-ycotx ? a. tan x C. sinx b.…

A: This is a question related to differential equation. Based on the formula of integrating factor we…

Q: Solve the differential equation by variation of parameters. y" + y = sin?(x) sinx ( sin’'x cos (x) +…

A: Solve the above questions

Q: Find a particular solution Y of the nonhomogeneous differential equation y 00 + y 0 + y = 2 cost −…

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Q: Obtain the differential equation of the family of circles with center at point (h,k) and radius r.…

A: The equation of the circle having a center (h, K) and radius and radius r is given by:…

Q: 2. Find the differential equation of the family of curves as described below. a. Family of circles…

A: As you asked multiple question I solve only the first one 2.a) We have to find out the differential…

Q: Find the particular solution to the differential equation y' + ytanx = sin2x with the given boundary…

A: Given:         Differential equation y'+ytanx=sin2x            y(0)=1 This is in the form:…

Q: solve the differential equation. tan2 y dy = sin3x dx                   when y(0) = 0

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Q: determine the general equation using bernoulli differential equation siny(x+siny)dx+2x^2cosydy=0

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Q: Obtain the differential equation of the family of circles having their centers on the x-axis.…

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Q: a. Circle of radius 1 and centers on the line y = x

A: The solution is given as

Q: y' cosx f. -=cos y

A: The given differential equation is,y'cos2x=cosy

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: Find the differential equation of the family of circles with fixed radius, r=a+b,and tangent to the…

A: I am attaching image so that you understand each and every step.

Q: find solution of this differential equation:  y′ tanx sin2y = sin^2 x + cos^2 y

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Q: y' + (2 tan x)y = - cos'x

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Q: 2. Find the differential equation of the family of circles having their center on the y-axis.

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Q: Solve using the non-exact linear differential equation  [ytan(x)(cos(2x))-1]dx+csc(2x)dy=0 when…

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Q: Form a differential equation by eliminating arbitrary Function. Z= (x + y)f(x² + y² ) %3D

A: Given z = (x+y)f(x2+y2)zx+y = f(x2+y2)                             (1) Partially differentiate with…

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: Find the solution to the differential equation that satisfies the given condition. I am having…

A: Given differential equation can be written as Integrating both sides , we get

Q: The function y(x) is defined by the implicit equation x2−√ylny=1. Find its differential at the point…

A: Differentiate both sides with respect to x and solve for dy/dx

Q: Find the curve y that satisfies the differential equation y' sin r and passes through the point (T,…

A: Integrating the equation

Q: Find the Differential Equation of the family of circles with center on the line y = x, and passing…

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Q: Find the differential equation of the family of circles with center at the origin. a+x y = .2 x'+1

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Q: (2xy-tan(y))dx-(sin(y)ln(5x+15)-y^(-1))dy=0 using Exact Differential Equation

A: Given,Differential equation,2xy-tan(y)dx-sin(y) ln(5x+15)-y-1dy=0To find: General solution of the…

Q: (3tanx-2cosy)sec²xdx

A: We will solve the differential equation.

Q: Obtain the differential equation of the family of curves described below. a. Circle of radius 1 and…

A: a) Given radius of circle r= 1 and center lies on y=x linewe know that circle equation is…

Q: 5. а) Find the derivative of y = (cosh r)*. Show that the function y = e -2" (sin 3x + cos 3.x)…

A: we have to find the derivative of the function y=(cosh x)x2

Q: Obtain the differential equation of all circles with center on line y = -x and passing through the…

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Q: Parabolas with axis parallel to the y-axis

A: Equation of parabola parallel to y-axis and having center(h,k) and having distance a from vertex to…

Q: Find the Differential Equation of (sin2x-2ycosx)dx=2dy

A: First we compare given differential equation with dy/dx+Py=Q and find integration factor using…

Q: Solve the differential equation by variation of parameters. y"+ y = sin(x) %3D x cos(x) y(x) =…

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Q: Write the first-order differential equation in standard form. (Use yp for y'.) y' = x7y + sin(x)

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Q: Solve differential equation (2y cos y - x sec y - x tany)dy = (1 + sin y) dx

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Q: 2. Obtain the differential equation having the solution as the equation representing all circles of…

A: The solution is given as

Q: Find the differential equation of all family of circles in which the center lies on the line y = -x…

A:

Q: Find a particular solution Y of the nonhomogeneous differential equation y'' + y' + y = 2 cost −…

A: Given a nonhomogenous differential equation y''+y'+y=2cost-sint

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

A: We have to find

Q: Circles with center on the line y = x

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Q: 2) Obtain the differential equation of parabolas with vitex and focus on the x-axis

A: To find: the differential equation of parabolas on the x- axis.

Q: Find the differential equation of family of parabolas with axis parallel to the x-axis and with…

A: The general equation of family of parabolas with axis parallel to the x-axis, with a vertex at a…

Q: 27. Obtain the differential equation having the solution as the equation representing all circles of…

A: The differential equation of all circles of radius 1 and centers on  y=x

Q: 1 Solve for the differential of y when y=sinx, x=÷, and dx=-

A: Solution. A is true.

Q: The linear differential equation y' - cotx + 3y csc x = 0 has the integrating factor tan A tan () B…

A: The objective is to find the integrating factor of given equation: y'-cotx+3ycscx=0

Q: Find the differential equation of the family of circles with fixed radius and tangent to the x axis.

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

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Q: Find the differential equation of all family of circles with center at the line 3y - x = 0 with h…

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