B-Solve the wave equation subject to the initial conditions (a) u(x, 0) = sinx (all x) (b) (x, 0) = 0 (all x) Use both the d'Alembert solution and the separation of variables method and show that they both give the same result.

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A:

Q: 16. Find the solution of the wave equation for the vibrating string that satisfies the initial…

A: See answer below.

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A:

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A: Given Wave equation: a2∂2u∂x2=∂2u∂t2 for 0<x<1 and t>0 Given Boundary conditions: u(0,t)=0,…

Q: he technique that we used to solve the time-dependent Schrodinger equation in class is known as…

A: The wave equation is given as:                                      ∂2yx,t∂x2=1v2∂2yx,t∂t2…

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A: Consider the given second order IVP u′′+0.25u′+4u=2 cos(3t), u(0)=1, u′(0)=−2.

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Q: Verify that the function 5x3 + 3t4 is a solution to the 2nd order differential wave equation.

A:

Q: Exercise 2.7 dy 2cosx-sin². -sin x+ y 1. Verify that y, = sinx is a solution to and solve the %3D…

A: Note:- As per our guidelines, We can answer the first question since the exact one wasn’t specified.…

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A:

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A:

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A:

Q: Y' + 3Y = 6e-3t cos6t + 24 ; Y(0) = 0,

A: The given IVP is as follows. Y'+3Y=6e-3tcos 6t+24, Y0=0 Apply Laplace transform on both sides of the…

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A: We have to solve the given wave equation.

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A:

Q: (a) Solve the Cauchy-Euler equation solution of the differential equation r²y" + xy + 4y = 0, r> 0.…

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Q: solve the following one-dimensional second-order partial differential equation. which is known as…

A: Given,          a2∂2u∂x2=∂2u∂t2, 0&lt;x&lt;L, t&gt;0…

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A: On solving this we will get:-

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A:

Q: Solve the initial value problem for r as a vector function of t. Differential equation: = - 24k dt2…

A: NOTE: Refresh your page if you can't see any equations. . take integration  ..............(1)

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A: Theware equationisoru2442С22at22x²variasles.retUcht) 2X (4) TLE)solve by separation ofo a 옖X'…

Q: Chapter 2, Section 2.2, Question 27b Solve the differential equation. Use the fact that the given…

A:

Q: both give the same result. both the d'Alembert solution and the separation of variables method and…

A: Here we use direct formula of d Alemebrt

Q: Q.5 Solve the wave equation: U₁=Uxx-ex-6x, U(0,1)=8, Ux(1,1)=3, U(x,0)=4sin ³x+ex+x³-ex+7 **********

A: Using separation of variables

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A: According to the given information, it is required to determine the value of constants.

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A: Given differential equation is u''−3u'+u=e3t.....1 We have to convert the given differential…

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A: First =&gt; Method of undetermined coefficient

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A: We will integrate the differential equation twice to get the general parametric solution of r(t) .…

Q: (E)- Exercise 1 Consider the differential equation: y6)-16y" 3-2e"+6r sin 2r By using the method of…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 18 -14 dx dt 21 -17 with the initial value x(0) %3D 9 x(t) LO

A:

Q: 2.20 Find the solution of the wave equation a?u dx? dy? y > 0 with initial data u(х,0) — 1 и, (х,0)…

A: For the solution follow the next step.

Q: Find the solution of the differential equation that satisfies the given initial condition. du 2t +…

A:

Q: A. Obtain the differential equation of the gi- (1) 3x² – xy² = c (2) y = a cos(x +B) (3) y = c,e¬2x…

A:

Q: Find the solution of the differential equation that satisfies the given initial condition. 2t +…

A: The given differential equation is dudt=2t+sec2(t)2u⇒2u du=2t+sec2(t) dt ..................... (1)

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A: The given Differential equation is tcost-sintx"+x'tsint-xsint=0

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A: A first order linear ordinary differential equation has the form of y’(x) + p(x) y = q(x)   The…

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A:

Q: a) Use the d’Alembert solution to solve Pu 4- -∞ 0 | u(x, 0) = sin x, uz(x, 0) = sin x. Simplify…

A:

Q: Exercise 1 Consider the differential equation: y®) – 16y" = 3-2e+Gr sin 2r By using the method of…

A:

Q: Exercise 1 Consider the differential equation: y6) –16y/" = 3–2e+6z sin 2r By using the method of…

A: Please see the answer in step 2.