Solve the 2nd-order linear non-homogeneous DE, y" + 36y=9e-9t subject to the initial conditions y (0) = 0 and y'[0] = -1, using Laplace Transform. Simplified form of Lapalace Transform Y (s) = The partial fraction form of Y (s) is Y (s) = The general solution of the non-homogeneus equation is = 0

Q: Application of the Laplace transform (Solution of partial differential Equations) учу where y(ost) =…

A: The given partial differential equation is ∂y∂t=2∂2y∂x2 where y(0,t)=y(5,t)=0 and y(x,0)=10sin 4πx

Q: Solve the initial value problem using Laplace transform y" – 4y'+4y= 3te", y(0)=4, y'(0) = 2

A: The given question is related with Laplace transform. Given that,                    y'' - 4y' + 4y…

Q: Use the Laplace transform to solve the given initial-value problem. y" +9y' = 8(t− 1), y(0) = 0,…

A: The initial value problemFrom the Laplace transformFrom the initial values

Q: Determine the constants a, p, yo and y'o so that Y(s) = Bs + C (s + D)² is the Laplace transform of…

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Q: (i) Beginning with the homogeneous version of ODE, find the characteristic equation by letting…

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Q: Solve by Laplace transform method x' = 2x – 2y у'3 х — у — cos t x(0) =,y(0) = 3 4

A: Solution: The system is x'=2x-2y y'=x-y-cost x0=35,  y0=45

Q: Use the Laplace transform to solve the differential equation, subject to the indicated initial…

A: Here we use basic definition of LP transform

Q: 6. (a) (b) Use integration or partial fractions to find the inverse Laplace transform of the…

A: The answers are given below.Explanation:

Q: x'+2y'+x=0, x'-y'+y=0, x(0)=0, y(0)=121

A: See solution in image Explanation:

Q: y" – 2y' + y = 0 y(0) = 1, y'(0) = 0 Solve the initial value problem using Laplace transform.

A: y"-2y'+y=0 Applying Laplace Transform and using the fact that it is linear we get Ly"-2Ly'+Ly=0…

Q: 5. y"+y' - 2y = 54te-2t, where y(0) = 6, y'(0) = 0

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Q: F{6f"(x) – 2f' (x) + 7f(x)} =

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Q: Use the Laplace transform to solve the given initial value problem. For technical reasons, write uc…

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Q: Solve the initial value problem using Laplace transform b) y" + 3y' + 2y = 2 8(t-3), y(0)=0,…

A: Laplace and inverse Laplace transform

Q: Solve of differential equations by the Laplace transform -2t x' - 5x -e ", x(0) = 3 %3| | |

A: The solution of the given differential equation using laplace transform is solved below.

Q: Solve the following initial value problem by using the Laplace Transform method. y'' − y' = ex,…

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Q: у" - 5у' + бу %3D7 УО) %3 2, у' (0) — 4

A: We use the following standard results to solve the given problem.…

Q: Use the Laplace Transform to find (1 the solution of the ordinary differential equation : y`+3y`-4 y…

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Q: Find the Laplace transform of the solution of the initial value problem 0<t<2 2 ≤t v (0) = = 1,…

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Q: - (D' - 4)y = x'e"

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Q: Solve by Laplace transform for the give ode 2x"(t) + 2x'(t) + x(t) = u(t), x(0)=0, x'(0)=0

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Q: (2 + V-9 )3

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Q: Q5) (a) Solve by using Laplace transform the partial differential equation 8², =9. y(0,t)= 0, y(2,t)…

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Q: Laplace under initial conditions x '+ y' + x= 0 and x '+ 2y' = 1 equation system x(0) = y (0) = 0…

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Q: Obtain the solution of the partial differential equation with initial conditions using the Fourier…

A: Given: d^u(x, t)/dt^2 = 9 d^2u(x,t)/dx^2    (-∞&lt; x &lt; ∞, t&gt;0)   u(x, t)=4e^(-5|x|) du/dt(x,…