Show that u(x, t) = sin wx sinh wt is a solution to Utt + Uxx = 0.

Q: Show that u(x, t) = 4 tan-1 I-ut ev where v is constant, is solution of Uxz – Utt = sin(u)

A: To check the given solution satisfy the given partial differential equation, substitute the solution…

Q: Find the general solution of the system of equations 2 -5 x' 0 = - ( ² = ₂ ) x + ( cost), 0 < t < *.…

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Q: 1. Consider the matrices A₁ 4 = ( 1 ) - 1 3 0 A₂ 42 = (3-2) ₁ 4₁ = ( 2² -2²), , A3 0 -2 These…

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Q: -2 cos(6t) dt J (10+4 sin(6t))²

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Q: Show that the function u(x,t) = sin(kx)sin(akt) is a solution to: utt = a²uxx where ut = a²u/at²,…

A: The given differential equation iswhere,Show that the solution to the differential equation is

Q: DON'T USE CHATGPT Solve the following equation by canceling operator y"+y = 3x sin(x) (In the answer…

A: First of all we find the auxiliary equation for the corresponding homogenous equation. Find the…

Q: V ss Vst Vts Vtt || || 11 11 V sin(2s² - 4t²)

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Q: Solve J²u = Ət² u (0, t) = u (x, 0) = J²u 4- 2 მ2 u (π, t) = 0 sin (2x), 0 0 (x, 0) = 0 Ju Ət

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Q: S 1+cos(3x)dx

A: Given : ∫1+cos3xdx

Q: Find the general solution to the linear ODE. Use each method (integrating factors and educated…

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Q: guess the form of the solutions 1- y’’ - 2y’ -3y = 3sin(5t)+tcos(5t)+2te^-t 2- y’’+2y+10y=4te^-t-…

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