(a) Solve the initial boundary value problem by separation of variables : Utt = 4u7z 0 0, u(0, t) = 0, u(n, t) = 0 u(x, 0) = sin(4r), u(r,0) = 0.

Q: 2. Solve the Initial - Boundary Value Problem, Ии — а?ии — 0, for 0<x< 1, 0 <t <o∞ u(0, t) и(1,t) %—…

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A: we have to check stability of critical points

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A: We have to determine the type and stability of the critical points of the homogeneous systems.

Q: , 0 0 u(0,1) — 0, и(п,г) %3D0 sinx, u (х,0) — 0 Utt = Uxx, u(х,0) 3D

A: Consider the solution: ux, t=XxTt and the conditions are X0=0=Xπ, T0=fx=sinx and T'(0)=0  uxxx,…

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A: Consider the given differential equation, ∂2u∂t2=-c2∂4u∂x4      ⋯1 Let us consider that…

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A: Solution ) we have option 3rd  y"+ 4y = 0 Auxilliary equation  m2 + 4 = 0 m2 = -4 m = √( -4 )  m =…

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Q: Solve the initial boundary value problem: = a?uz u(0,t) 0 r(1, t)hu(1, t) = 1 u(x, 0) = sin(Ta

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A: In this question, we solve the differential equation using initial conditions.

Q: A rectangular steel sheet is bounded by the axis -0y-0,x-a and y b. The temperature along the edge…

A: Steady state heat equation.

Q: Hiwo- solve the hyperblic partial differential equation numericaly where d²u d²u dx² = with initial…

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A: NOTE: According to guideline answer of three subparts can be answered for other please ask in a new…

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Q: 11. Solve the initial-value problem dx = -2x – 2y dt dy -2x + y. dt where the initial condition (x…

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Q: HW: Solve the Partial Differential Equations by using separation of variables method: Ut - 4uxx = 0…

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Q: HW: Solve the Partial Differential Equations by using separation of variables method: U1 – 4uxx = 0…

A: From the given conditions, answer is not correct. Please check the whole questions and answer.

Q: 3. A coupled mass-spring system is described by the differential equations x = -x, + x2 x- 2x, = 0…

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Q: What is the solution of given initial value problem? =y + sin t dt2 da + cost dt - dt2 * (0) = 1, a…

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Q: Consider the boundary value problem (BVP) d² u du +2u = 0, dx² dx (1) -3. u(0) = 0, u(1) = 1. Using…

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Q: 3. Solve the heat equation ди 2- +2 | with the boundary conditions u(0, t) = 0, and u(T,t) = 0 %3D…

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Q: 2- Find the solution of the partial differential equation =u, -2 with boundary conditions u(x,0) 0…

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Q: The solution of the initial boundary value problem * U, = 4u, u (х,0) - 0, u, ( x,0) = x(1– x),…

A: Given, utt=4uxx…

Q: 11. (a) Show that is a solution of the system satisfying the initial condition X = sin t - t cos st)…

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Q: 2.23 Determine the solution of the heat equation ди a?u 0 <x < 1 at ax? with boundary conditions…

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Q: Consider the equation u; = uxx – 9u, 0 0, with boundary condition u(0, 1) = 0, u(1, t) = 4 sinh(9),…

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Q: (a) Find and classify all the equilibrium solutions for the given differential equation 3 = y – y –…

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Q: 1. Solve the inhomogeneous heat equation du Drta, 00 %3D Ot with initial condition u(z,0) = "-= %3D…

A: The PDE is homogeneous if f = 0 (so l[u] = 0) and inhomogeneous if f is non-zero. Some examples of…

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Q: Consider the boundary value problem, 0<x< 0<y< 2 0 < y< ax2 ay2 u(0, y) = y² – 1, u y) = 0, 0<y<…

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Q: Let u (x, t) be the solution of the initial-boundary value problem Ut 0 0, Uz (0, t) = uz (4, t) =…

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Q: Solve the initial-boundary value problem Utt = 16uzz u (0, ) u(π, t) 0 u(x,0) = E sin(nx) u:(x,0) =…

A: ∂2u∂t2=16∂2u∂x2u=XT . . . . (1) Where X and T are function of x and t. ⇒∂u∂t=XdTdt,…

Q: 4. Solve the heat equation du +et sin(3.x) with the boundary conditions u(0, t) = 0, and u(7, t) = 1…

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