Given the differential equation y" +9y = e-7t, y(0) = 0, y′(0) = 0 Apply the Laplace Transform and solve for Y(s) = L{y} Y(s) = 1 (s+7) (s² +9) OF Now solve the IVP by using the inverse Laplace Transform y(t) = L¯¹{Y(s)} y(t) =

Q: Using the linearity of the inverse Laplace transform, solve for the solution of the differential…

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Q: Solve the simultaneous ODES (a) (b) y"(t) + y'(t)- 2y(t) = sin t., x'(t) + x(t)- 3y(t) = 0 -

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Q: Consider the following initial value problem: x" 5x14x = sin(8t), x(0) = 2, x' (0) = -1. Using X for…

A: In your answer this will be 696 place of 632

Q: 2) Use the Laplace transform to solve the differential equation y' + y' - 2y = -4; with initial…

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

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Q: y'' – y" + 4y'- 4y = 10e-t, y(0) = 5, y'(0) = -2, y"(0) = 0 %3D %3D

A: Given differential equation is y'''−y''+4y'−4y=10e−t, y0=5,y'0=−2 and y''0=0 Take Laplace transform…

Q: Consider the following initial value problem: x" - 5x²14x = sin(8t), x(0) = 2, x' (0) = -1. Using X…

A: We will use Laplace transformation table  f't  = s Fs− f0f'' t= s2 Fs − s f0 − f0Lsinat=aa2+s2

Q: Employ Laplace transforms to solve the differential equation of y"-2y'+y=3e¹* Given y(0)= and y(0) =…

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Q: Solve the ODE by the Euler method: given 2y" = -4y' - 1.5y y(0) = 3 and y'(0) = −2.5 with step h =…

A: To find- Solve the ODE by the Euler method: 2y'' = -4y' - 1.5y       giveny0 = 3 and y'0 = -2.5with…

Q: When the differential equation y" + 2 y' + y = x (e)^(- x) given y (0) = 1 and y'(0) = - 2 is solved…

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Q: Using the linearity of the inverse Laplace transform, solve for the solution of the differential…

A: We have to find a solution to the given differential equation.

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: y(t) = y" - 7y' + 6y = et + s(t - 7) + 6(t-9), y(0) = 0, y'(0) = 0 ) + ( [ ])2(x-7)+ ( [ 1) 2(t-1

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Q: Given the differential equation y'' + 3y' – 3y = sin(3t), y(0) = -2, y'(0) = 2 - Apply the Laplace…

A: Given that, the differential equation need to solve it using the Laplace transformation.

Q: Given the differential equation y"-4y'-y = 2 sin(5t), y(0) = 2, y'(0) = −1 Apply the Laplace…

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Q: Consider the following initial value problem: x(0) = 2, x' (0) = -1. Using X for the Laplace…

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Q: Solve the following systems of linear differential equations using the Laplace transform x" +x' + y…

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Q: Find a 4th degree differential equation whose solution y(t) satisfies L{y(t)} = Y (s) = 1/ (s^4 +1)…

A: Formula for Laplace transformations L{0} = 0 L{a·f(t)+b·g(t)} = a·L{f(t)}+b·L{g(t)} here a and b are…

Q: Solve differential equation using Laplace transform ý + 3ý + 2y = 4 with y (0) = 0, ý(0) = 1

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Q: Using Laplace Transforms Method, solve the following Differential Equations 1. y' = 2et with y(0) =…

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Q: post office sells 4-cent sheep stamps and 2-cent sunset stamps. Cole bought 5 stamps spent exactly…

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Q: Solve and prove that the solution derived from Laplace Transform of Derivatives and the initial…

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Q: Given the differential equation y'' + 5y' – 5y = - 4 sin(4t), y(0) = 2, y'(0) = 0 Apply the Laplace…

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Q: Consider the IVP y" +3ty'-6y=6,y(0)=0,y'(0)=0 (1).What is the Laplace transform of the differential…

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Q: Determine the solution of the differential equation uring Laplace Transform y" + y + 5/4y - 1-u (t -…

A: The given differential equation is: y''+y'+54y=1-ut-πy0=1, y'0=-1 We have to determine the solution…

Q: y' = xy³ (1 + x²)−¹/2, y (0) = 1

A: y'=xy3(1+x2)-12  dydx=xy3(1+x2)-12given  y(0)=1∫xndx=xn+1n+1+c