2. Obtain the differential equation having the solution as the equation representing all circles of radius 1 and the centers on the line y = x.

Q: x'y" – xy' = Inx

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Q: 2. Form a Differential Equation for the given equation y = 2 cosx + 5 sinx by eliminating the…

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Q: y = C, cos 3x - C sin(-3x)

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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: (30. y4) +y" = 0; 1, x, cos x, sin x, (-, 0)

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Q: Find the differential equation of the cubics : cy^2= x^2 ( x - a ) with a held fixed.

A: Here c is arbitrary constant and a  is fixed. So we have to find a differential equation which does…

Q: B. Solve for the differential equation of the following families of curves: (1) Family of parabolas…

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Q: Given the differential equation of the family of circles with radius of 2 units and whose center's…

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Q: B. Find the differential equations of the families of curves. 5. Straight lines with slope and…

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Q: equation

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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: Find the general solution of the differential equation y′ = tan3 3x sec 3x

A: Given: y' = tan3(3x)sec(3x) =>dy/dx = tan3(3x)sec(3x) =>dy = tan3(3x)sec(3x) dx

Q: 1. Draw and obtain the differential equation of a circles having its center on the line x =y and…

A: 1.

Q: Find the Wronskian of two solutions of the differential equation ty" -t(t-5)y' + (t-3)y=0 without…

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Q: Show that the differential equation UTM dy -2 - ye rey - 2y dr is exact and find its solution.

A: Use the concept of exact differential equations.

Q: Q1 By eliminating the constants A and B from the equation y = Asin 2x + B cos2x, form an ordinary…

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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: y > Ae* +Be* +ce; A,B and c unstant are

A: As per our guidelines we can solve only one question at a time please upload unsolved question…

Q: Suppose the auxiliary equation of a homogeneous linear differential equation has roots m_1=-2 and…

A: We have given the root of the auxiliary equation which is m1=2 and m2=+-2i

Q: (3x-y+6)dx + (6x -2y-6) dy=0 hint: Case 1

A: Given differential equation is                    (3x - y + 6)dx + (6x - 2y - 6)dy = 0

Q: Find the general solution of the differential equation. Use C, C1, C2,⋅ ⋅ ⋅to denote arbitrary…

A: Consider the given differential equation: y'x=4tan2x-3cosx Here, the objective is to find the…

Q: y= 4 + Inx; xy'

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: State where in the ty-plane the hypothesis of the (non-linear) Existence and Uniqeness Theorem is…

A: Given: The given differential equation is y'=t-y2t+5y

Q: 4. Form the first-order differential equation of y = e(sin y + r) %3D

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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: Find the differential equation of all circles passing through the origin and having their centers on…

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Q: Q2 Form a differential equation from the function y = (4– 2 cos x) x)cosx.

A: Given below the detailed solution

Q: 4. Solve the differential equation d'y d’y 1 dx dx by the method of variation of parameters extended…

A: A differential equation is an equation that involves derivatives or differential coefficients or…

Q: Solve the differential equation using only methods taught in class. y' + 3xe' = 0

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Q: - ydx + (x ++ Vxy )dy= 0

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Q: 5. Obtain the differential equation of the family of circles with center at point (h,k) and radius…

A: Please refer to the image below

Q: 4. Find the Differential Equation and Orthogonal Equation of the family of parabolas with vertex and…

A: Let the vertex lies at (a,0) and focus at (b,0) So the general equation of parabola having axis as…

Q: The degree and order of the differential equation 1+ is = dy dz о 12, 1 O 1, 15 O 15, 1 O 3, 1

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Q: Obtain a linear differential equation with real, constant coefficients that is satisfied by the…

A: If the particular solution is: y=2excos3x                                        ....(1) The first…

Q: Find the homogeneous differential equation whose general solution is y = 3cos(x) - e3x/2 -…

A: Given the solution of a homogeneous differential equation   y = 3cos(x) - e3x/2 - 4xsin(2x) Find the…

Q: The solution of the differential equation 2r -y = 3 represents a family of O circles straight lines…

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

A: General equation of differential equation.

Q: 1. Find the differential equation of the family of circles of radius r whose centre lies on the…

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: Find the equation of the line tangent to y = x2 – 3x – 5 and parallel to the line y = 3x – 2.…

A: Explanation of the answer is as follows

Q: y' + (2 tan x)y = cos³ x = COS" X

A: The correct answer is option (I) , i.e.  y = (cos²x)(c+sinx) The detailed solution is as follows…

Q: (2x+3y-5) dx + (3x-y-2) dy=0 hint: Case 2

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Q: Find the terminal value, lim y (r), for the solution of differential equation dy + 3z'y - 6z". dr

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Q: Find a differential equation whose general solution is -4t y = cjet + cze¬4.

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Q: Write the general form of Cauchy-Euler differential Equation. Solve the follow- ing differential…

A: General form of Cauchy-Euler Differential Equation. The differential equation…

Q: Solve the first order differential equation using any acceptable method. sin(x) dy/dx+(cos(x))y=0,…

A: We have given First Order Differential Equation,

Q: (4) Form the differential equation by eliminating the arbitrary constants a and b from y = aeª +…

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Q: Find the homogeneous linear differential equation whose solution is y=-e^(3x/2)-4x sin⁡2x.

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Q: Obtain the Differential Equation of all circles passing through the origin and (0,8).

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Q: Find the solution of the differential equation that satisfiesthe given initial condition.

A: Given: The differential equation y'tanx=a+y with initial condition yπ3=a for 0<x<π2. To find:…

Q: y"-4y = 0; cosh 2.x, sinh 2x

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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.