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: State whether the following statement is true or false: A vector space may have two or more zero…

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Q: Solve using MUC. y" +4y=3sin2x 3+3+5+ y = C₁ cos2x+ C₂sin2x - -Xcos2x 4 y=C₁ cos2x + C₂sin2x +…

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Q: y" + y = sec x tan x

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Q: Hiw/ Find F'(x) 1. if F(x) = x, tanx 2-if y = Sinx it casx 3- Find g" ()if y co) = Sec y ex) g ex)…

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Q: find dy/dx y = | Vx V 1 5) 1+x 20) y=Cof"| 1-x, 15) y = \tan /2x + 7

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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: If u = x3 -3xy and v= 3x2y-y3, prove that Pu/Əx2 + Pu/əy2 = Pv/ax2 + Pv/@y²

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Q: what is the general solution of x tan²y dx + (1+√x) dy =o

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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: Find Domain and Range бяц tue Ⓒsin (x+3) +2y x²+2y 3x + y² 3) 3x + Sin (3x) +2y+Z² Ⓒ x+2y cos2x…

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Q: y" + y = sec x tan x

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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: Find the general solution of y''' − y'' − y'+ y = 1 + sin x + sin 2x + ex

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Q: What is general solution of v = ds/dt if v = 2/t^3/2? a.-4/t^1/2 = s^2 + c b.-4/t^1/2 = s + c^2…

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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: tan x= Sin 2X

A: Given: y'+y tan x= sin2x

Q: Show that: 2 2 4: +2} | sin 2y x=1 y=vx TOX dydx = 2y dydx+ _3 x=2_y=vX

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Q: find dy of X sin 2y =YCO52X

A: Given: x sin 2y=y cos 2x To Find: To find dydx.

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: In integrating the function fx* in Sx dx using integration by parts, what would you choose for your…

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Q: 5) S V2 + sin 3t · cos 3t dt

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Q: S 1+cos(3x)dx

A: Given : ∫1+cos3xdx

Q: Obtain the general solution using variation of parameters (D²+3D+2)y=cos(e^-x)

A: We have to solve the given differential equation by variation of parame

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

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Q: 1/2 yee? +4 dy +17y=0 dx2 when Pove then ydy that Sinzx, %3D0 dx

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Q: Find the solution. dy 2y + dx -=x²y²sinx 1 (A) y = х? (sinx - c) B y = x ( sinx +c) y = x²(cosx+c)…

A: We have to find solution of given D. E.

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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Q: Salve 6y"o)-5y'Lx)+Yx)= esinx+ cos2X with

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