6) Find the general solhution to the fourth order differential equation is equation "whose"' characteristic

Q: 1. Show that separable differential equation is exact differ- a ential equation.

A: separable equations are always exact, since by definition separable equations are of the…

Q: 7. Sketch some of the family of curves of the differential equation :

A: Given : The differential equation dydx=-y2x. To sketch : some of the  family of curves of the given…

Q: The Cauchy -Euler equation is a a differential equation with variable coefficients. صواب İhi

A: The Cauchy - Euler equation  is a linear homogeneous ordinary differential equation

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: 3. Find the differential equation of a family of parabolas with axis parallel to the x-axis.

A:

Q: Obtain a differential equation associated with the primitive Ax2 + By2 = 1

A: See answer below.

Q: 4. Obtain the Differential Equation from the family of curves of the form

A: We need to find the Differential Equation for the family of curves y=Cx for which we need to…

Q: The Cauchy -Euler equation is a a differential equation with constant coefficients.

A: yes this is true because A second order Cauchy-Euler equation is of the form…

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: 4. Find the differential equation of a family of parabolas with axis parallel to the x- axis.

A:

Q: Obtain the differential equation of the family of curves described and sketch some members of the…

A: We will find differential equation of the given condition.

Q: Consider the first order differential equation

A: Given, the differential equation,                          1xndydx=y2(x)where n∈ℕ.

Q: Define Differential Equation (DE) along with 2 examples?

A: A differential equation is an equation which contains one or more terms and the derivatives of one…

Q: Find the differential equation of all straight lines at 2- unit distance from the origin.

A:

Q: Give the differential equation of family of lines passing through (2,0)

A: Let the equation of  line be y= mx + c Now if the line pases through (2,0) then  0= 2m + c --> c=…

Q: (ye Cn2

A: Using the exactness property of differential equations.

Q: the given Cauchy-Euler equation to a differential equation with constant coefficients. (U

A:

Q: 5. Obtain the Differential Equation from the family of vertical parabolas whose vertex is at (h,k).

A: Formation of the differential equation

Q: By climinating the arbitrary constants, form the differential equation in the fotowng cases: 1- y2 A…

A:

Q: Find the differential equation of the family of circles with centers on the line x – 2y = 3 and…

A: Given:  circles with centers on the line x – 2y = 3and passing through (3, 0).

Q: What is the differential equation of all parabolas with axis parallel to the y-axis?

A:

Q: Obtain the differential equation of the family of straight line with the algebraic sum of the…

A: The differential equation of the family of straight line with the algebraic sum of the intercept…

Q: 9. A particular solution of the differential equation whose slope field is

A: Given:

Q: Find the differential equation of the family of cuves and draw at least three members of the family…

A:

Q: Obtain a differential equation associated with the primitive Ax^2+By^3=9

A: Differential equation is obtained by eliminating the constants A and B from the primitive equation.…

Q: 1. What is the integrating factor of the differential equation ydx – xdy = 0 using case 1?

A:

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

A:

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

A:

Q: Find the differential equation of all family of straight lines at a fixed distance p from the…

A:

Q: Find the differential equation of the family of circles with center on x-axis.

A:

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: Explain thesteps to obtain the general solution of a 2nd order homogenous One Differential Equation?…

A:

Q: 3. Show that the differential equation zxy

A:

Q: Obtain the differential equation of the family of lines passing through (-1.1).

A:

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

A:

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

A:

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 the Families of Circles with center (2,k) and with radius r.

A:

Q: Find the ordinary differential equation of a circle which passes through the points (0,0) and (2,0).

A: We will find out the required differential equation for given circle.

Q: Find the differential equations having as solution; all tangent lines of parabola y2 = 4x .

A: Here, we have to find differential equation of all tangent planes of parabola

Q: Obtain the differential equation of the 5. Family of straight lines with x- intercept and slope…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

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

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: Obtain the differential equation that describe the family of curves.

A: The general equation of the circle isx-h2+y-k2=r2where (h,k) is the center of the circle and r is…

Q: Solve the Cauchy-Euler differential equation on the interval (0, ∞). ry" +6x²y" + 4xy' - 4y = 0

A:

Q: If the family of curve has 4 arbitrary constants then the corresponding differential equation is c)…

A:

Q: find the differential equation of a family of parabolas with an axis parallel to the x-axis

A: We have to choose the correct answer from the given option according to the given condition