=0 in (0,0) and T(x,t)= 0 at x= 0, l for all te[0,0).

Q: у" — Зу' + 2у %3D2е3t y(0) 3D 0 у'(0) — 4 |-

A: Given differential equation is  y''-3y'+2y=2e3t given condition is  y(0)=0 ,y'(0)=4

Q: Consider the function z=x ln(1+ y“), if x=2-t and y=\t , use an appropriate form dz of the chain…

A: According to the given information, consider the given function z.

Q: Solve the differential equation using the Laplace transform у" — 5y — бу %3Dеs", y(0) 3D 0; у' (0)…

A:

Q: Let z = cosh t. Find the differential dz when t = In 3 and dt = 0.2 O 4/3 O 4/15 O 8/15 O 1/3

A:

Q: The differential equation 3zy" – 2y + 7y = tan x is normal on any open interval not containing = 0.

A: The main objective is to determine the given statement is true or false.

Q: 10. Find the linearization, L(x,y,z) of the function f (x, y, z) = e* + cos(y + z) at Po (0,",").

A:

Q: The differential equation is as follows: d[RL] -[RL]k2 dt with initial conditions, [RL], = [RL];=0…

A: So, we will have to use [ RL ]0  as a value in here, and hence, it will be treated as a constant.…

Q: Use the method of reduction of order to find a second independent solution of the given differential…

A: Use reduction of order method

Q: A solutipn of the Ordinary Differential Equation x'y" - 2xy' + (x? + 2) y = 0, x > 0 is defined by…

A:

Q: (a) express dw/dt as a function of t, both by using the Chain Rule and by expressing w in terms of t…

A: Express dw/dt as a function of t by using the Chain Rule. Use the sum rule and split the bracket.…

Q: Use Laplace transforms to solve the differential equation de +4-+ 40 = sin (8t) dt d? given that 0…

A:

Q: Use Laplace transform to solve the partial differential equation: 8² y dy dx² at +xt where y(x,0) =…

A: Solution

Q: Show that the process X(t) = A cos At + B sin At (where A and B are RVs) is wide-sense stationary,…

A:

Q: х. у 2) w=¨+2,x= cos“(t), y = sin°(1), z =-, at t = 3 Z Z t

A:

Q: Use at least two methods to prove that dr/dt=0 when r=√x2 + y2, x=α cos t, and y=α sin t if α is a…

A: First method   r=x2+y2r=(α cost)2+α sint2            since x=α cost and y=α sint  =α2cos2t+α2sin2t…

Q: Find the temperature u(x, t) in a rod of length L, if the initial temperature is f (x) = 100 sin 6nx…

A: Given function is, fx=100sin6πx at x=0 and x=L Now, we know that, ∂2t∂x2+qgk=1α·∂t∂z....(1)

Q: Use Laplace transform to solve the differential equation -2y + y = 0, with the initial condition…

A: The Laplace transform of the function f(t) is represented as F(s) or L[f(t)], it is defined as…

Q: 2/3 1/3, Z=x (44х, + 6Y-3.1) X

A: To find total derivative of z=x123x21344x1+6Y-3.1

Q: Let z = tan-1(E) – In(cos y), where r = T- u and y = uv. Use multivariate chain rule to find the…

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: Use Laplace transform to solve the partial differential equation: d'y dy ox² at -+xt where y(x,0) =…

A: The given P.D.E is ∂2y∂x2=∂y∂t+xt where yx,0=0, y0,t=0 and yx,t is bounded for t>0 and x>0. To…

Q: HeWal Compute yG), for the differential eguahion

A: The Laplace transform is a particularly elegant way to solve linear differential equations with…

Q: f(x) = In(2 + cos x). -2.125, xk+1 = Ik +0.5, yk = f (xk), k E N To = %3D %3D = 0r

A: The function is fx=ln2+cosx Conditions: x0=-2.125, xk+1=xk+0.5, yk=fxk, k∈ℕ xk+1=xk+0.5…

Q: Find the temperature u(x, t) in a rod of length L, if the initial temperature is f (x) = 100 sin 6nx…

A:

Q: 31 Calculatea Riemann Sum for the function h(x) = 2 + sin x , over x e [1,5], with n = 8 I(T-1)

A:

Q: Q4. Find the temperature distribution in an infinite circular plate with circular hole of radius a…

A: ℝr,θ:a≤r≤∞,-π≤θ≤π and ua,θ=sin3θwhere ur,θ is periodic and satisfy the continuity condition.and…

Q: of Let f (x, y) = tanh-¹(x-y) with x=e" and y= usinh (t). Then the value of dt (u,t) =(4, In 2) is…

A:

Q: Find the temperature u(x, t) in a rod of length L, if the initial temperature is f(x) = 100 sin 6Tx…

A:

Q: Let w = x°e4y cos(9z). Find the value of dwldt at the point (3, ln 5, 0) on the curve x = 3 cos(t),…

A: Given: w=x6e4ycos(9z)x=3 cos(t)y=ln(t+5)z=6tDifferentiating we…

Q: A) If w = 2 y et* – In z where x = In(t² + 1), | dw y = tan-1 3t and z= e3t. Find by Chain Rule dt

A:

Q: e) Suppose that W= √√x² + y² + z², x= cos 0, y = sin 0, z = tan 0. dw T Use the chain rule to find…

A: According to our company's guidelines I can only answer (e), since (e) and (f) are not inter…

Q: 1. Use the differential df to approximate the change in the value of f(x,y) from the point (1,0) to…

A: We will be using definition.

Q: y" + 5y' + 4y = 0, y(0) = 1 y'(0) = 0

A:

Q: 8. Let f(x, y) = cos(y – x) and r(t) = (e', e2t). Find if (r(t)) at t = ln(3).

A: The solution is given as

Q: The Bessel function of order 0, y = J(x), satisfies the differential equation xy" + y' + xy = 0 for…

A:

Q: Let z= 28x + 32xy - 8y , where x(t,s) = cosh (4t) cos (5s) and y(t,s) = sinh (4t) sin (5s). ze at…

A: Here, z=28x2+32xy-8y2

Q: Use the method of asymptotic expansion to find the asymptotic solution of the differential equation.…

A: We will use the basic knowledge of ordinary differential calculus to answer this question completely…

Q: Q1) suppose that W= x2+y2+z² and x cos 0, y = sin0, z = tan 0 ,use the chain rule to find de when 0

A: We have, W=x2+y2+z2 and x=cosθ, y=sinθ, z=tanθ  We have to find, dwdθ=? at θ=π4

Q: |1) Use a sine expansion to compute the solution of ( ди д'и at ôx? u(0,t)=u(1,t) = 0,t > 0, u(x,0)…

A: According to the given information, it is required to compute the solution of the given equations.

Q: dy Solve the differential equation using Laplace transform y = sin h(2t),given that y(0) = 0, /(0) =…

A:

Q: use the Laplace transform to solve the differential equation y"(t) + 4y(t) = h(t), with y(0) = 2 and…

A:

Q: (a) express dw/ dt as a function of 1, both by using the Chain Rule and by expressing w in terms of…

A:

Q: A:= {(x, y) € R² :1< log(x) < 2}. = {(x, y, z) E R³: sin(xy² + «/2) · cos(z) = 1} . (a) Decide…

A:

Q: 3. Find the total differential of the ff. at (1, -1). f (x, y) = 3.x² + y² – xy %3D

A: Solution:Givenf(x,y)=3x2+y2-xyFormula:d(xn)=nxn-1

Q: Q2:- a. b. Let u=x²-2xy + 2y³ with x = s²ln t and y = 2st³. Find au/as and au/at. find the total…

A: We need to solve the two questions.

Q: b- Use Chain Rule to compute w = 2y e* - Inz } əw at x = ln(t² + 1), at (t) equal to (1) for: y =…

A:

Q: Q1) Suppose w =÷+ ?, x = cos² t, y = sin² t, z = ; Evaluate dw at t = 3, by using the Chain Rule dt

A: