1) Find a function y whose graph passes through the point (1, and satisfies x?y' = y.

Q: y=8sin(x)cos(x) ; x=pi/3

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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: find a particular solution yp of the given equation. primes denote derivatives with respect to x.…

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Q: 1- Find the equation of the tangent to the curve y = 2 sin x+ cos2x at the point x = n. 2- Find the…

A: Solution:

Q: 1. Find dy/dx if cos 4y+ysin x =3 2. Use implicit differentiation to find the slope of the tangent…

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Q: find a particular solution yp of the given equation. primes denote derivatives with respect to x.…

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Q: I FIND THE SECOND DERIVATIVE OF THE FF IN ITS SIMPLIFIED FORN 3x-4 1. y = Arctan 2. y = 2 Arccos (1…

A: y=Arctan3x-44

Q: 23 Find dy/dx on the graph y3 sec/x2 + y2 = cos2x at point (1, 2).

A: Use product and chain ruleof differentiation at given value

Q: Calculate differential: f (x) = = e-* cos(3x) + 2 of the range [1,2] with h=0.05 a) Using the…

A: Equation is f(x)=e-xcos(3x)+2.Numerical differentiation method to find the solution.The value of the…

Q: Find the 4th order differential of the function y=√2x+1.

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Q: 2. What is the largest possible area of a triangle with its base on the x-axis between x= 0 and…

A: The given curve is y=sinx. To find the largest possible area of the triangle with its base on the…

Q: Obtain the differential equation for the family of circles with center on the line x = 8.

A: The general equation for a circle can be written as

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

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Q: The tangent line to the curve y = x3 at the point (1,1) will intersect the x-axis at x = a.2/3 b.…

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Q: Prove that the function y = ecos* satisfies the differential equation: y" + sin(x) y' +y cosx = 0

A: Find y' , y" and put into given differentiatial equation.

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 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: 2. Find dy/dx by implicit differentiation: 5x^2y+5y^2x=-3

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Q: 1. Find the y" of y = (4x - 3x + 1) (5x + 7) 2. Find y" given y = cosx + sin 3x 3. Find all the…

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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: Find the differential equation of the family of parabola with vertex and focus on the x-axis

A: The given question is related with parabola. We have to find the differential equation of the family…

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

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Q: 8. Find the length of the curve y = e on the interval 0, ln 2| %3D

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Q: Compute the indicated derivative using the chain rule. X = 4 + 3t, y = -7t; Oy

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Q: # 5) Find the extrema points for the function f (x) = using the second derivative tes 1+x x2 %3D Fon…

A: To find the extreme points.

Q: find a particular solution yp of the given equation. primes denote derivatives with respect to x.…

A:

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: 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 at the origin. a+x y = .2 x'+1

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Q: 11. Find the length of the curve x = on the interval (2, 4] (integrate with respect to y) 12y3 un

A: Given that the function x =y55+112y3 Find the arc length of the graph of the given curve on the…

Q: 23.3 Use centered difference approximations to estimate the first and second derivatives of y = e*…

A: The formula for the first derivative of a function fx at x=a by centered difference approximation is…

Q: What is the c value obtained for the special solution of the equation under the initial condition y…

A: Here we have to find constant of integration c.

Q: b) Find derivative of the following: 1. y= 5x° + 2x -x + x* -9x+12 y=1-cos 20+3sine iI. ii. s= xln…

A: The detailed solution is as follows below:

Q: 3) Suppose 2X z = xe cos 3y, find all the first and all the second derivatives.

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Q: 1- Solve the second derivative forf(x, y,z) = e sinay3) əx2

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Q: 11. Find dy/dx of In(x² + y²) + 2 arctan

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

Q: Find the differential equation of the family of parabolas with vertex ar Focus on the x-axis * O y =…

A: We have to find

Q: Find the equivalent differential equation for all tangent lines of the parabola y = x^2

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Q: tan(4x + 8). Find the differential dy when x = Let y 1 and dæx 0.3 Find the differential dy when x =…

A: In the given question we have to find dy of the function at both of the given value.

Q: Calculate differential: f(x) = e-* cos(3x) + 2 of the range [1,2] with h=0.05 Using the backward…

A: Equation is  f(x)=e-xcos(3x)+2.Numerical differentiation method to find the solution.The value of…

Q: 1- Find the equation of the tangent to the 2(x2 + y2)2 25(x2 - y?) at (3,1) 2- Find dy/dx for y =…

A: (1) given equation is                                              2x2+y22=25x2-y2,   at (3, 1)…

Q: find a particular solution yp of the given equation. primes denote derivatives with respect to 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 third order derivative of y = In(cos(2x))". A. y' = -40sec²(2x)tan(2x) B. y' = -80sec…

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Q: Find y(1) for y" = - 4z - 4y, X, = 0, yo = 0, z, = 1, with step length 0.1 using Euler method (2nd…

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Q: Evaluate the integrals

A: Given integral is:

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

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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

Q: find the differential equation of circles with center on the y-axis

A: