3. Consider the wave equation with =R²U₂ -∞00 Utt === u(x,0) = sin 2x, u(x,0) = sin 3mx. Use d'Alembert's solution method to determine the solution of the above equation.

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A: (a) Consider

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A: NOTE: Horizontal axis is t-axis  .

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A: To solve the given problem, we have to apply the method of undetermined coefficients. Note:- From…

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A: The differential equation is:To Do:Determine the characteristic equation and solution to the given…

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Q: 4. Calculate leme/) at (z,y) = (a, 4). sin(z/g) ey2/2 A ev2/2 B 4

A: Here we have to calculate ∂∂xesin(x/y)=? at (x,y)=(π,4)

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Q: Consider the wave equation 00, with (0,r) =(71) = 0, m(x,0) = sin x and -0 at -0. Then is

A: Given wave equation, ∂2u∂t2=3∂2u∂x2 , 0<x<π, t>0withu0,t=uπ,t=0andux,0=sin x, ∂u∂t=0 at t=0…

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A: The given differential equation is, dydx=16x25y and condition y(0)=-3. A differential equation is…

Q: Solve PDE : 1 Urr + -Ur + 2u 1 zU00 = 0, 1<r< 3; ВС: u(1,0) = 3, u(3, 0) = sin(30). %3D

A: Given, PDF is               urr+1rur+1r2uθθ=0,        1&lt;r&lt;3;        (1) and  BC:…

Q: ㅠ [sin(y) sin sin (y) sin² (y) 1+ cos(y) dy KIN

A: We will use substitution method to integrate.

Q: 3.8. Question. Match equations y' = sin x, y' = cos y, y' = y cos(x)· a) c) b) to direction fields.…

A: To find the direction field of a differential equation you first need to isolate y' from the…

Q: y'47y'+12y = 2le", y(0)=,0)=-10 .

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Q: Use method of successive approximation to solve the Deifferential equations up to 3 substitutions…

A: , We have to solve differential equation using successive approximation method.

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A: We have to choose the correct answer

Q: (a) Solve the inhomogeneous 1st order equation Uz - Ut = cost U (x, 0) = 0.

A:

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A: We will find out the required solution.

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Q: 6. Find * : y- + 5)ao TK, (b) y = Sin 5x I+cos 5x dx

A: Solving the problem by finding the derivative.

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A: The given differential equation is y''+2y'+y=2e-x1-xsin 3xy''+2y'+y=2e-x-2xe-xsin 3xHere the…

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Q: Solve the inhomogeneous wave equation on the real line Utt − c2Uxx = sin x, x ∈ R U(x, 0) = 0, Ut(x,…

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Q: (v')3 -3(v')2 +18y-36x+58=0 1-)Find the singular (outlier) solution of Lagrange's equation

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Q: Find the general solution to the following 3-by-3 linear system: 1 -5 10 2 -4 8 X. dt 3 -5 8.

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

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A: