a) If u=(x,7), where x = 0(1) and y=p(1), then that %3D prove du du dr ди dy dt Əx dt ây dt If x=rcose, y=rsin 0, then show that a'e 0. Əx

Q: A particle of mass m is moving in a one-dimensional region of space where there is a Coulomb-like…

A:

Q: 4. z = tan-'(y/x), x = e', y = 1 - et

A:

Q: Suppose w = In(x² + y² + z²) , x = ue³" sin(9v) , y = ue3" cos(9v), and z = ued". %3D Compute dw/du…

A: If w is a function of three variables, such that w(x,y,z) and x, y and z are further function of u…

Q: b) Use Laplace transform to solve the system of differential equations dr 4y, dt dy dt +x = y + 3e*,…

A:

Q: Let x and y be differentiable functions of t, and lets = √(x2 + y2) be the distance between the…

A:

Q: Suppose that r(t) = cos³ t i+ sin³ tj+et k, show that d dr (r.- dt dt d?r X at2 dr d'r. r.at at3…

A: Given: rt=cos3t i+sin3t j+e-t k we have to show that ddtr·drdt×d2rdt2=r·drdt×d3rdt3

Q: Apply runge kutta method of order two on du/dx = sin(xu), u•=0.1,h=0.1 to find u(0,3)

A:

Q: Suppose that z = xy² and x and y are differentiable functions of t with x = 1, y = −1, dx/dt = −2,…

A: Given  z=xy2 Also at t=-1 x=1y=-1dxdt=-2dydt=3

Q: 2. When object P, with mass m, , moves at v, and object Q, with mass m,, moves at v,, the velocity…

A: Given,For P, mass = m1  and velocity = v1Let, velocity after collision is u1For Q,mass = m2 and…

Q: 8. Find the flux of F = (2x – 5y², 3y, x) out of the sphcre of radius 2 centered at the origin.

A: The flux of the vector space is given by the formula, ∫S∇.F dS where S is the sphere of radius 2…

Q: þ/ Show that the function satisfy Laplace equation f(x,y) = In /9xy+3y² Q/ find by using chain rule…

A: Since you have posted multiple questions ,we solved the one question for you  To get the solution of…

Q: In(xy) cos(Tx + T) when x 2 and y = 1/2.- Find the tangent plane to f(x, y)

A: We have to find the equation of  tangent plane.

Q: Glven: XY and ZW Intersect at polnt A. Which conJecture Is always true about the glven statement?

A: as given that XY ↔ and ZW↔ intersect at point A. so, here we understand few terms which is given in…

Q: Q2) A) Verify that wxy wyx for w x sin y+y sin x +xy. %3D R) Show that f(x v) = e-2y cos 2r…

A: See the details solution in below

Q: Let h(y) = In(y In y). Find h' (y). Show your work.

A:

Q: If F= represents the flow of a liquid through a parabolic cylinder S: y=x, 0sxs2, 0szsl. That is…

A: If F→=y2,-x2,z2 represents the flow of a liquid through a parabolic cylinder S:y=x2,0≤x≤2,0≤z≤1.…

Q: 1. Verify that (t) = et, y(t) = e' satisfies the system %3D dx 3y3 dt dy y, dt %3D

A:

Q: Determine the displacement u(x; t) of systems modelled by the following differential equations azu _…

A: The given initial-boundary value problem is of the form uxx=utt, 0<x<L,…

Q: Which among the following is NOT a LINEAR first order differential equ O (1+ cos 0) de sin 8 (sin 6…

A: Given that: 1. Linear first order differential equaiton.                  2. dydx+ln(x+1)yx=x3yk

Q: dz 또는 dt dw 1. 연쇄법칙을 사용하여 -를 구하여라. dt (1) z = xy + x² y, x =1+21, y =1-2 (2) z = /x²+y°, x = e', y=…

A: Given

Q: 4. Find the work done by the force field F = (x? sin(y),y) on a particle that moves along the cubic…

A: Given: The force field, F→=x2siny,y on a particle that moves along the cubic y=x3 from 1,1 to 2,8.

Q: Calculate the work done by a constant force field F on a particle that moves once uniformly along…

A: Given, path of the curve x^2+y^2=1 & F(x,y)=(αx,αy)

Q: Assume x and y are functions of t. Evaluate dt for 2xy - 2x + 4y3 = - 56, with the conditions = -…

A: Given      2xy-2x+4y3=-56 →           1      dxdt=-16, x=4, y=-2

Q: Let X, Y be jointly Gaussian, standard, and Cov (X,Y) = y. Find pdf of Z = X +

A: Answer:-  Given that, X and Y have jointly Gaussian distribution.

Q: (a) 3y' In (u) dy

A: We will use the ILATE rule in this example to solve the integral and for solving we use the formula…

Q: Consider the slope field shown. (a) For the solution that satisfies y(0) = 0, sketch the solution…

A: Given,  the slope field :

Q: a) i. Express in terms of the unit step function, the piecewise continuous causal functions 0 5…

A: Since you have posted a question with multiple sub-parts, we will solve only first three sub-parts…

Q: Exercise (1): Determine the order and degree of the following differential equa- tions: (1) y - 4x +…

A:

Q: If a and ß are positive constants, show that the particular solution of dy %3D У (В — ау) dt that…

A:

Q: Show that the displacement u(x, t) in an elastic string of length t fireed at both ends which is set…

A:

Q: dt dx2 dy , ди u(0, у, 1) dx (1, y, t) = 0, и(х, 0, г) %3D ди - (х, 1, г) %3D 0, dx и(х, у, 0) %3D 2…

A:

Q: Consider solving the autonomous differential equation dy = f(y), te [to,T], y(to) = yo %3D dt with…

A: First we will define what is the meaning of error and then truncation error. Error means there is a…

Q: Complete the table: Varsep Homo Exact Linear Linear Bernoulli Bernoulli in t (Bt) Differential…

A:

Q: The differential operator Lis defined by d (e* 一 Ly = -e*y · - - dx dx (a) Determine the eigenvalues…

A: Given : Differential operator L is defined by…

Q: Study the following delay differential equa- tion (Find conditions on c1 and c2 to in- vestigate the…

A: If C1≥C2, Then the steady state : N*=1C1+C2 is asymptotically stable, for all delay τ≥0

Q: dx axy with r, K, a, s, b>0. dt 1) Find all steady-states for this model, and analyze their…

A: Given ,dxdt=rx1-xk-axy    anddydt=sy1-ybx  with r,K,a,s,b>0          To determine all…

Q: 10. Para resolver la siguiente ecuación diferencial: y" + 2y' + y = 0 con y(0) = 1; y'(0) = 1 Se ha…

A: The solution of differential equation is given by using Laplace transform and partial fraction…

Q: Let y 4x + 3x + 4. If Ax 0.3 at a = 3, use linear approximation to estimate A %3D Ay =

A:

Q: dw Let w =xycosz, where x = t°, y =ť, and z = arccost. Find dt

A:

Q: If the input x(t) and the output y(t) are connected by the differential equation dy(t) T + y(t) =…

A:

Q: What does Cauchys EU theorem guarantee for The IVP:  dy/dt = -(y)^2/2t,  IC: (to,0)

A: Ft,y=-y22tDomain:{t,y∈R2:t≠0}∂F∂y=-ytDomain:{t,y∈R2:t≠0}∴function Ft,y is continous.So there exists…

Q: Assume x and y are functions of t. Evaluate dy / dt for 4xey = 8 - ln 64 + 6ln x, with the…

A:

Q: 06/ Let w = z - sin(xy) where x = t y = In(t) z = et-1 Find dw/dt by :- a- Using Chain Rule…

A: The given is related to application of differentiation and application of partial differentiation.…

Q: -if f₁ (t) properties of Fourier transfor eat alt) JF.T = $ fit) ējut dt = - feat. ejust dt е ماز-…

A: Topic:- calculus

Q: Hnew ³ Let w=f(u) + 9 (v); where u = x+iy and V=X-iy, show that w satisfies the Laplace eap. Wxx +…

A:

Q: Let x and y be differentiable functions of t, and lets = √(x2 + y2) be the distance between the…

A: Given equation is s=x2+y2. Compute the derivative of s with respect to t.…

Q: find du/dt for u=4ysin(x)+xze^xy^2 and x=3s+t, y=ln(s+t), z=cos(st)

A: The objective is to find  dudt, where u=4ysin(x)+xzexy2, x=3s+t, y=ln(s+t), and z=cos(st)

Q: What does Peanos EU theorem guarantee for the IVP:  dy/dt = -t/y ,  IC: (to,0)

A: Peanos theorem: "Consider the initial value problem y1= f(t,y), y(t0)=y0. Let f: Domain f →Rn. Then…

Q: 2. The Jacobian, J of a robot hand at a particular time is given. Calculate the linear and angular…

A: Consider the given  Jacobian  J and joint velocity.…

Q: a) Without doing any calculations, state whether the vector field: er sin2(xy) F = -V 1 + x*y4 is…

A: (a) Since ∇×∇=0 So, curlF=0 Hence, F is conservative field.