Solve the following IBVP: Utt = 4uzz 0 0, u, (0, t) = u,(27, t) = 0, t>0, u(x,0) = 0, 0

Q: find the genecol solution of Cauchy EuLer equation

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Q: Estimate the root of following nonlinear equation x – 2x – 1 = 0 using Newton-Raphson method…

A: (a) The given equation is f(x)=x4-2x-1=0 find the derivative f'=4x3-2 initial guess x0=-1…

Q: Find the perticular number or orthogonal trajectories of x2+cy2=1 passing through the point (2,1)

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Q: Cauchy-Euler equations have unique solutions at x=0, specifically the function y = 0.

A: Solution:-

Q: For the equation uxx + uyy = 0, write the necessary equations which can be used to solve the…

A: The Laplace Equation: ∇2U=∂2U∂x2+∂2U∂y2=0   ⋯1…

Q: (5) Find the particular solution passing through the point (1,8) How does this solution behave as t…

A: Sol

Q: 16. Of all points (x, y, z) that satisfy 3x + 4y + 2z = 52, find the one that minimizes (x – 1)2 +…

A: Let f(x,y,z)=x−12+y−42+z−22   and    g(x,y,z)=3x+4y+2z−52≡0Apply Lagrange Multiplier method to find…

Q: Let 47x + 20 y = 2 is a linear Diophantine equation 1) Show that 47x + 20 y = 2 has integnl…

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Q: Find a homogeneous LDE with constant coefficients that has y= - 3xsin2x as a particular solution.

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Q: What must be the measure of ZX in order for ARST to be similar to AxYZ?

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Q: The integration expression Jsin(3In(x)+ 4)cos(3In(x) + 4)dx must be transformed into using suitable…

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Q: Expand x'y + 3y - 4 about the point (1, -2) by Taylor' s theorem.

A: Let, the given function be fx,y=x2y+3y-4 and the given point is 1,-2

Q: Use Euler method to approximate the value of y(0.1), given y' - x2 - y = 5, y(0) = 3 with Ax = 0.025…

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Q: 8) Find the family Coff esponding to of orthogonal trajectories y=kx".

A: To find the orthogonal trajectories corresponding to below curve.

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: x²y" +xy' – y = T

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Q: general

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Q: Use Euler method to approximate the value of y(0.1), given               y' - x2 - y = 5 ,  y(0) =…

A: Euler Method:-  For a function fx, y the method is xi+1=xi+∆xyi+1=yi +h fxi, yi; i=0, 1, 2,... Here,…

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

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Q: A stretched string of length 20 cm is set oscillating by displacing it midpoint from the rest…

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Q: When does an nth order, homogeneous, Cauchy-Euler equation anty(n) + an-1tn-ly(n-1) + +aity' + aoy =…

A: Given: nth order To find: Cauchy-Euler equation

Q: To compute the predicted values of Y, Y, we need (do not assume you have the fitted model already):…

A: To find the predicted values of Y, first we have to fit the model.

Q: Find 2. dy of 2.

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Q: Find the largest t-interval where the solution to the IVP (t − 5)y'' - cos(t)y' + y = 2/t,  y(1) =…

A: Consider the provided question,

Q: 1. 2xy'+ xy'+ (x² 3) y=O a) Show thet a regulor singulerity Xa>0 is point. 6) Use froteniaw method…

A: (a) Given equation, We know that,

Q: 5) Form a DE by eliminating the arbitrary constants from the equation y = asin(4x + 1).

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Q: Suppose that the share of total production consumed by player i is x / x+(n1)y, where is player i's…

A: The utility to player 1 is given as: u=xx+n1yAnw-x-n-1y;w>0,A>1 Also, Ak=Aw-x*

Q: Give two examples of the situation with the solution clearly and in order Soperties of Bessel's…

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Q: O DE Linitial condelim) dy -48-7x y)= 1 +2

A: we have to find the diifferential equation dydx=4x2-7x3y2+2    with initial condition y(1)=1

Q: what are the independent and dependent variables of this problem? is the DE separable?

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Q: Use Euler's method to estimate y(8) to estimate the solution to y' = y – 2x, y (0) = 1 %3D Use n = 4…

A: Given differential equation is y'=y-2x, y(0)=1.

Q: Show that y=lnx is a solution of xy’’+y’=0 on interval (0,∞) but is not a solution on interval…

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Q: Obtain the particular solution for: 2y" +2y=2sinx y(0)=0, y'(0) =1 By using method of variation…

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Q: Consider finite difference method to approximation the solution to BVP on 1. 2 y" = -e y(1) = 0 y(2)…

A: Given: The boundary value problem, y''=-e2y on 1,2 with the boundary conditions y1=0 and y2=ln2.…

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: Consider the follow ing LP model: max z = 50x, +100x, X +x, 5 300 | 2x, +x, 5 400 St. X, S 250 X, X,…

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Q: ly 3)[e^(-2y)]dy

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Q: Find valume bounded by abave Z:4-20 and below by Z-xy 2.

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Q: 3z2+x 30. If z – xz – y = 0, prove that- =- ax dy (3z²–x)³*

A: Let's find.

Q: Use the method of variation of parameters to produce a general solution of the inhomogenous equation…

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Q: Calculate •3 2x -dx et – 1 - -3 by Gaussian quadrature with n = 3.

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

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Q: SOLVE FOR THE ORTHOGONAL TRAJECTORIES X'(3k-x) - ky = xy

A: Take first derivative and eliminate k.

Q: Find the general solution to the DE using the method of Variation of Parameters: у" — Зу" + Зу' — у…

A: The solution is given as

Q: Estimate the In (1.1) and sec (0.1) Using a linear approximation and without using any kind of…

A: f(x)=ln(x) f'(x)=1/x f(1)=ln(1)=0 f'(1)=1/1=1 linear approximation is then L(x)=f(a)+(x-a)f'(a)…

Q: 7. y" -y' = 2sin 2x

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Q: 2. Solve Un Uxx X> 0,t> 0 with initial and boundary conditions given as u(x,0) = 1- exp(-x), u(x,0)…

A: The D'Alembert's solution of one dimensional wave equation whose charactertics lines are ξ0=x-ct and…

Q: The integration expression sin(3In(x)+ 4)cos(3ln(x) + 4)dx must be transformed into using suitable…

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Q: I Sdve for dydx using the four-step rule 2. Y = x- x 2.

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