Calculate . (x² + x²)e²as, where S is the cylinder with equation x² + y² = 9 for 0 < z < 10.

Q: Solve the following boundary value problem: uxy + Ux = 0, u(x,0) = +2, u(0,0) = 2 = cos (x)

A: To find- Solve the following boundary value problem: uxy + ux = 0, ux, 0 = cosx + 2, u0, 0 = 2

Q: Find a general solution of each reducible second-order differ- ential equation xy" + y' = 4x

A: We have to find the general solution of the given second order differential equation.

Q: Find the family of antiderivatives for each ofƒ(x) = ex, g(x) = 4x3, and h(x) = sec2 x.

A:

Q: H.W: Evaluate the integral (x²y - 2xy) dydx 1. 30 0-2

A: As per your query the solution of the question no 1 is given in the next step.

Q: Solve the following homogenous PDE du Pu with the nonhomogenous boundary conditions uz(0, t) = 0,…

A: We have to solve the given homogenous PDE.

Q: In the figure, ZY = ZX and YZ is produced to T. Prove that YT> XT. Y

A:

Q: Find the G.S. about x, = 0 for the following DE's 1. (x² + 4)y" + 2xy' – 12y = 0

A: As per our guidelines we can answer only first question and rest can be reposted

Q: By the even extension method applied to the function f (x) = e¬16x, where x > 0, the value of the…

A: We have to solve given problem:

Q: Find the coefficient of the following te zy in (z + y)*

A: A binomial expression is an expression of the form a+bn. By the binomial theorem this expands to…

Q: Solve for the particular solution of the following non-homogeneous DE. y''+y=2x

A: This question is based on solution of differential equations.

Q: Solve the following forr W=4xc for c %3D C = (Type an exact

A:

Q: find the general solution of the following 2. X Ux +y Uy +t Ut =xyt %3D

A:

Q: for which the sys y +z = 6, 4x + Ay = -5 has infinitely m a root of which qu: %D :

A:

Q: find the Solehion dy'= 4t + 2e

A: Given the differential equation :

Q: Please answer in pen

A:

Q: Find a ≤ b such that

A: ∫abx2-9dxApply the Sum Rule:…

Q: The identity LiS L xyzdzdxdy = "/2 S Sa rsin@cose zdzdrd® x² +y² 1-y² x² +y² is

A:

Q: general

A:

Q: If ƒ (0) = 1, ƒ (1) = 2, ƒ(2) = 33, f(3) = 244. Find a cubic spline approximation, assuming S" (0) =…

A:

Q: For the elliptic curve y^2 = x^3+ 4x, compute Np and ap for p = 3, 5, 7, 11

A: Let E be a nonsingular elliptic curve defined over a finite field with p elements. Then the number…

Q: 10 Suppose z = x + 2i and u=3+ yi where x, y E R. Find the smallest positive value of x z + u for…

A: Given z=x+2i and u=3+yi

Q: Find the value of the following tanh-1  ( 1 + 3j)   Partial Ans.    0.0919 + 1.2678i

A:

Q: Use the Intermediate Value Theorem to show that the following equation has at least one nonzero…

A: Given That,  Sec(2x)= 3^x

Q: 3. Show that the equation for G(r,ø) can be separated by choosing G(r,ø) = R(r)P(ø) into OR Rar ar 1…

A: Introduction: The Laplace equation is one of the most important partial differential equations. It…

Q: Use the substitution x = et, to solve the following Cauchy-Euler equation: x²y// – 4xy/ + 4y = x³ In…

A: We will find out the required solution for given Cauchy Euler differential equation.

Q: Find the G.S. about xo = 0 for the following DE's (x²+4)y" + 2xy' - 12y = 0 1.

A: Please see the below pictures for detailed solution.

Q: The general solution to: y'' – y' + 4y = 0 %3D is: y(x) = %3D Typle c_1 and c_2 to get c1 and c2 and…

A: We have to find the solution

Q: The equation 2x²y" +3xy'-(1+x)y =o has a regular singular point at x,= o %3D

A: The differential equation of the form, a(x)y''+b(x)y'+c(x)y=0 has a regular singular point at x=x0 ,…

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: X+ xy B. Evaluafe the tripe in tagral S5* xy dydzdx,

A: As we know that: The Power Rule: ∫xndx=xn+1n+1+C ; n≠-1 (B). From the given integration:…

Q: (4) Recall the formulac: (5) Find the integrals: • ftan² (x) dx t: Is ta SC

A:

Q: 4. Solve the equation ди for x E (0, L) and t > 0, for the following boundary conditions: u(0, t) =…

A:

Q: Given y = Va In æ , what is dy dr In z+2 In z+y7 dy dr dy dr In z-2 dy In z-I dr ||

A: Given,

Q: Calculate 1₁ ₁² ² a feas = e¯² ds for the piece of the cylinder x² + y² = 16 for 0 ≤ z ≤ 7.

A: we have to find the ∬Se-zdS for the piece of the cylinder x2+y2=16 for 0≤z≤7

Q: For the equation af = k at with boundary conditions f(x = 0, t) = f(x = 1, t) 0, and initial…

A:

Q: メpr t! prove that : d = (s«k-tank)

A:

Q: Find a general solution of each reducible second-order differ- ential equation y" = (x + y')²

A:

Q: For Z= x²csc y,prove that Zxy is equal to Zyx

A: Given that,    z=x2csc y

Q: 2. Find the following. 5 – xy? Zy if z = 3x + Y

A: For a function in two variables, the partial derivative with respect to a variable say x can be…

Q: 1. Solve Laplace's equation inside a rectangle 0 0 and H > 0), with the following boundary…

A: Given, Laplace's equation                    ∂2u∂x2+∂2u∂y2=0                   ...(1) (0≤x≤L,…

Q: Solve the following DE, using Separable method. y'In ly| +x*y =0.

A:

Q: Determine by inspection two solutions of the at least given first Order IvP. zzy, y (0) zo

A: To determine by inspection at least two solutions of the given first order IVP.

Q: 2 I| ysin(xy)dydx Н.W.

A:

Q: Find a general solution of each reducible second-order differ- ential equation y" + 4y = 0

A:

Q: Solve for the particular solution of the following non-homogeneous DE. y''-2y'=ex

A:

Q: 2. Let exp(z) = 2 + i find z in x + iy form. 3. Find the solution of In(z) = – T.

A: use: ln(x+iy)=ln|x+iy| + arg(x+iy)     where, arg(x+iy)=tan-1(y/x)

Q: Let y(x) be the solution of y' = y − 4x such that y(1) = 1. Using a step size of 0.5, set y0 =…

A: I am attaching a picture where you will get step by step solution first I write the formula of euler…

Q: Solve the following boundary value problems using the finite difference method -2xy - 0, y(0) -0,…

A: Given,      y''-2xy=0, y(0)=0, y(1)=1, with h=0.25