Which is the linear differantial equation into which the Bernolli differantial equation transforms

Q: Use linearization to determine an approximation of V1002.

A:

Q: 7x – 4xy = C

A:

Q: Find the orthogonal trajectories of the family of curves y=Ce* +10

A:

Q: Find all second-order partial derivatives for the following. z = 7ye6x

A: Given that z=7ye6x. Obtain first partial derivative. ∂z∂x=7ye6x'=42ye6x∂z∂y=7ye6x'=7e6x

Q: Determine ? such that ?′′(?) = 12? − 1 and 1 is both a critical number and a y- intercept of ?.

A: A differential equation is an equation in x,y and derivatives of y.  A linear differential…

Q: Compute the partial derivatives: = Z +y? || ||

A: Partial derivatve is

Q: Find the equation of the normal line (NL) to the graph f(x)=x³ – 4x atx = 3 .

A: We need to find derivative.

Q: 5Find the Orthogonal trajectories of the family of r=aeº

A: Question:- Find the orthogorial trajectories of the family of r=aeθ ?Solution :- We have r=aeθ -(i)…

Q: Use the composite trapezoidal rule to find approximations to I = (t- cost) dt with n= 1, 2, 4, and…

A: The composite trapezoid rule: ∫abf(x)dx=h2f(a)+2∑i=1n-1fxi+f(b), where h=b-an,xi=a+ih,i=0,...,n The…

Q: . Form the differential of the system of circles touching the y-axis at the origin.

A: The solution is given as

Q: The linear approximation of e is

A:

Q: 4) Find the orthogonal trajectories of the family of curves

A:

Q: 4. Find the orthogonal trajectories of the family of curves y= Ce“ + 10

A: Here we have to find the orthogonal trajectories

Q: Find the partial derivative. f(p, q) = ev af

A: From the given problem; fp,q=e6pq As we know that: The chain rule: fgx'=f'gx·g'x The Power rule:…

Q: Find all the second order partial derivatives of dx дудх ду

A: Since you have asked multipart question, we will solve the first 3 subparts of the question for you…

Q: الموضوع was althe eauation XÝY-2* Ý+4.=2* is a Linear differential Eauation and Heterogenious Dtrue…

A: The given statement

Q: Find the orthogonal trajectories of the given family of curves x - 4y c.

A:

Q: Determine the orthogonal trajectories of the family of electric field lines described by the family…

A: Given    x-c3+y2-c23x-c=x3   differentiate  w.r.t.x    3x-c2+2ydydx-3c2=3x2⇒2ydydx=3x2-3x-c2+3c2…

Q: find the orthogonal trajection of the family of curves x2+y2=a2

A:

Q: Show that, as n → ∞, n^4/3^n → 0 linearly with rate 1/3.

A:

Q: Find the orthogonal trajectories of the following family: y = Ce-x

A: First differentiate then  solve

Q: Find the particular soluti y' + 3x²y = 3x² %3D Initial Condition: y = 6 %3D

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Q: Determine the equation of the sinusoidal regression function for the data. X 25 30 y 140 125 0 120 5…

A: Sinusoidal Regression Sinusoidal regression finds a trigonometric model that gives the curve of best…

Q: Find the orthogonal trajectories of the family y = 1 - sec?r + C 4

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Q: Under the MSE criterion, we want to find the best linear prediction model for Y3 based on X: Y3 = ߢ…

A:

Q: Use least-squares regression to fit a straight line y = f(x) = Ax+B  to:   xi -8 -3 0 4 6 yi 7 4 2…

A:

Q: Find the orthogonal trajectories of the family of circles passing through the points (1, −2) and (1,…

A: Given that

Q: The orthogonal trajectories of the families of curve 3x? + y? = a? is

A:

Q: Give the family of orthogonal trajectories for the equation: y2 = Cx5+5

A: To obtain the family of orthogonal trajectories for the equation: y2 = Cx5+5. Find a differential…

Q: Find the orthogonal trajection of the family of curves x2+y2=a2

A:

Q: Find all the second partial derivatives of Z and show complete solutions Z= xy3ln( 3xey )

A:

Q: 5) Construct a linear approximation of the function f(x ) = lacX+s) about the point x,= 1. Compare…

A: Tangent line approximation or linear approximation is very significant in differential calculus.…

Q: A researcher collected data on ( X , Y ), and wanted to test if the true relationship is linear.…

A: To test whether true relationship is linear or not, consider Lack of fit F-test. H0: There is no…

Q: The partial differential equalion formed to om the (x -af + ÿ +(2-65 = 16 is nelation 9. %3D = 16

A:

Q: 2. Find the normal equations to the curve 2* = ax + bx + c %3D 2 = ax+ bx + c

A: Apply normal equation formula as below

Q: 2. Show that cos(wt – B), coswt, sinwt are linearly dependent functions of t. Show Complete Solution

A: Given that: cos(wt-B), coswt, sinwt

Q: By utilizing Gradient Descent where initial x1=x2=Dx3%3D0, What is the approximated min. point of…

A: To find - By utilizing Gradient Descent where initial x1 = x2 = x3 = 0, What is the approximated…

Q: Find the orthogonla trajectories of the family of the curve r = csine

A: Family of curves: r = csinθ

Q: 4. Find the orthogonal trajectories of the family of curves y= Ce“ +10

A: Given that, Family of curves is following, y = Ce2x + 10…

Q: a Find the Orthogonal trajectories of the family of r =; 1+coso

A: we need to find the orthogonal trajectories of the given family of the curve in the polar form.

Q: 5. Find the orthogonal trajectories for a family of circles tangent to the y - axis and centers at x…

A:

Q: Find the four second partial derivatives. z = 6x2 + y5 a2z дхду дудх ду?

A: We will find all the asked second order partial derivatives as following.

Q: For the family x² + 3y2 = c, find that member of the orthogonal trajectories which passes through…

A:

Q: 4) Find the orthogonal trajectories of the family of the curves x² = 2y – 1+ ce¬2v.

A: Given information : Family of curves :  x2 = 2y -1 +ce-2y

Q: Determine the order and degree of the differentiah equation y + ( )* dt

A: Using definition of order & degree of Differential Equation.

Q: Find the orthogonal trajectories of the family of curves ey + 2x2 = k.

A: Given,  ey+2x2=k

Q: Find the orthogonal trajectories of the given family of curves x^2 + y^2 = c^2. *

A: Curves:  x²+y²=c²

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.