dw Find and if w = x' + ln () + v, x = u² - "+ 5 and + y, x = u2 -+5 and y = 3v + 5u and point (v,u)=(2, 2)

Q: f(x, y) = ln (2x) In (3y) + x - y - xy - 3, then fyz (2,-) is equal to

A: Given :fx,y=ln2xln3y+x-y-xy-3

Q: du/dt = (1/ln(t+u))  -1

A:

Q: give a problem and solution for differentiation rule of exponential and logarithmic functions in…

A: The solution for the above question is as shown below.

Q: If x+y divided by x-y= x^2+y^2 and dx/dt=12, then what is dy/dt when x=1 and y=0? show all work…

A: Given thatx+yx-y=x2+y2x+y=(x-y)(x2+y2)  [cross multiply]x+y=x3+xy2-x2y-y3

Q: If the source function (the right hand side) of a differential equation whose characteristic…

A:

Q: Find the differential equation of straight lines with slope and x –intercept equal.

A: Recall:  The equation of straight line is y=mx+b where, m=slope, b=y-intecept   Given, slope and x…

Q: A company will sell N units of a product after spending $x thousand in advertising, as given by N =…

A: We are given that N=50x-x2, 5≤x≤25. Now, dN=50-2x dx. First, increase the advertising budget from…

Q: Estimate ln(0.9) using a linear approximation

A: Given:ln(0.9)

Q: he population y(t) of a certain microorganism grows continuously and follows an expo uadrupling time…

A: In this question, the concept of derivatives is applied. Derivative We can use a derivative to…

Q: A toxic chemical accidentally released into the environment from a metal processing plant degrades…

A:

Q: Classify the entangled differential equation and find its general solution. y′ = xcosecx + y cotx

A: The given differential equation is of the form of  linear differential  . General form of linear…

Q: When the linear differential equation is multiplied by an integrating factor the equation will…

A: Answer of given question is written in below steps.

Q: y = Arctan√3x−4/4 2. y = 2 Arccos ( 1 -x/2) + √4x − x2 3. y = ln (x3(x−1)/(x−2)^2) 4. y…

A: d2dx2arctan3x-44=d2dx2arctan3x-42=ddx1x3x-4=-9x-82x23x-43x-4…

Q: Find the differential equation of the family of curve Straight lines with slope half the value of…

A: solutionGivenstraight line y=mx+CAlso givenslope =m=dydxC= y interceptat x intercept, y=0Also given…

Q: If f(x, y) = ln(x + y), then total derivative or total differential of f at x = 3 and y = 20 is : Y

A: Given data: The given expression for the function is f(x,y)=ln(x+y). The given value of x is x=3.…

Q: 3) Find the solution af equation that satisties the qiven mitial condition. of the differential L0…

A:

Q: differential equation of the family of circles whose center is on the line y = 3x

A: Please refer to the image below

Q: USE EXACT DIFFERENTIAL EQUATIONS To SOLUE THE $OLLOWING: In dx-tn(x=2) 'पर्क - डेण बर =0 y dy dx 3D0…

A:

Q: A bank pays continuous compounded interest. Sue deposits $100 in the account and in 3 years she has…

A: We will find the equation of A(t) as following.

Q: What is the differential equation obtained by eliminating the parameter A from the relation y = A +…

A:

Q: The differential equation ry" + 3y - 7y=seca is normal on any open interval not containing a = 0.…

A:

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

A: Given:

Q: 5. Find the derivative of y = In(cos v3x + 2 ), by using chain Rule.

A:

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

A:

Q: y ln x - x ln y = 1

A: ylnx-xlny=1Treat y as yx

Q: al csc x y cotx

A: We have to find the intregating factor of given differential equation.

Q: 6. Why is it very easy to conclude that x2 dx diverges without making any integration calculations?

A: This question is taken from the calculus and sub-topic is improper integral in which we have to give…

Q: Take first and second derivatives of y = xr, y=(ax2 + bx + c)2, y=ecx, y=e-cx, y=ln(x).  In all…

A:

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

A:

Q: Suppose f is differential equation on (-inf, +inf), f(3)=12 and f'(3)=-2 use linear approximation to…

A:

Q: Find the differential equation of family of lines whose angle of inclination is 60 degrees.

A:

Q: Find general solution of differential equation. Enter transient terms if any. x^2y' + xy= 7

A: Here we will find out the required general solution for given differential equation.

Q: In a city of a fixed population of " people , the rate of change (with respect to time t) of the…

A: Given Data: A city has a fixed population is P. Also given, the rate of change (with respect to time…

Q: Classify the differential equation 4 4 4 = 0

A: An ordinary differential equation is an equation containing independent variables, dependent…

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

A:

Q: A normal is drawn at a point P (x, y) of a curve, it meets the x-axis at Q. If PQ is of constant…

A: We will show that the given differential equation describing such curve is correct and will find the…

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

A:

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

A: See solution below

Q: These equation classifies by dy 3 +5x y dx' tan x dx Ordinary Differential Equation O Partial…

A: By see tha solution of this question

Q: Sketch the slope field and some representative solution curves for the given differential equation.…

A: We are given the second order linear differential equation. y"=x+y. or  d2ydx2=x+y....(1) We need do…

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: (a) By using the chain rule and the derivative (1, if x>0 4 (1xl) ={-1, if x<0 %3D find (lx-x) vxE…

A: Use the chain rule to differentiate the above given function and than use the given derivative of…

Q: Find the genprat Sotoution of the differential equation 3x+2 2y

A: By using the Separation of Variables Method.

Q: The differential equation governing the decay of a certain radioactive substance through time is dq…

A:

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

A:

Q: After a correct transformation of variable, a homogeneous differential equation will be reduced to a…

A: We have to check given statement true or false

Q: Consider the differential equation = 5 - y. In a coordinate system with window [-3,11] by [-4,10],…

A: Consider the equation

Q: Calculate the truncation error to solve the differential equation: Yi+1¬Yi = Xị → (*) Ax dy Instead…

A: Follow the following solutions to get the complete correct answer.

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.