Find the Laplace transform Y(s) of the solution of the given initial value problem. Then invert to find y(t). Write uc for the Heaviside function that turns on at c, not uc(t). y" + 9y= e−2tu3 = y(0) 0 y'(0) = 0 Y(s) = y(t) = -3s e (8+2)(+9)

Q: Solve the differential equation using Laplace Transform. (b) y" – y" + 4y' – 4y = 10e-t, y(0) = 5,…

A: We will find out the required solution.

Q: Transform the differential equation -2y + 4y = cos(at) y(0)=-6 into an algebraic equation by taking…

A: The differential equation is: -2y'+4y=cosat; y0=-6. We have to transform the given differential…

Q: Solve the differential equation y" + 4y' + 3y = e-t, y(0) = 1; y'(0) = 0 %3D %3D using Laplace…

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Q: (x' = x- 2y V = 5x – yi x(0) = -1, y(0) = 2. %3D %3D %3D %3D

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Q: Classify the following ODE y(4) -3y (3)-y' =0

A: We have to classify the ode

Q: 31+2 dy - of the function y= dt 7. Find +4 dy of the function y = 5 tan (6x)+ log, (36x² + dx 8.…

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Q: Consider the initial value problem y" – 5y' – 4y = sin(t) y(0) = 5, y'(0) = 2 A. Use the Laplace…

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Q: 3. Find the solution of the following ODE: xy' + 8y = 12x y y(1) = 16.

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Q: Show that the transformation z = log tan (x/2) reduces the differential equation d²y +cotr +4x…

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Q: Use the Laplace transform to solve the given initial-value problem. y"+ 2y"-y'- 2y = sin(4t), y(0) =…

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Q: Q3. Use the Laplace transform to solve the initial value problem (4) y" - 8y' + 15y = 9te²t, y (0) =…

A: Since you have posted a multiple question according to guildlines I will solve first(Q3)   question…

Q: Q3.(a) Solve for the general solution using the method of variation of parameters: 3y" + 6y'+ 3y =…

A: Given the equation 3y''+6y'+3y=x2ex 3D2+6D+3y=x2ex Auxiliary equation is 3D2+6D+3=0…

Q: Draw the hyperbola with the equation: 3x2 − 2y2 + 6x − 8y = 6.

A: Given the equation of the hyperbola : 3x2-2y2+6x-8y=6.

Q: D. Solve the differential equation using Loaplace transform of y" + y = 6sin 2t ; when y(0) = 3 and…

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Q: sider the following initial-value problem. y' - y = 2 cos(2t), y(0) = 0 d L{f(t)} for f(t) = 2…

A: Laplace and inverse Laplace transform

Q: x* (t) – x(t) = 4 cost with x(0) = 0, x' (0) = 1 %3D y = 2e with y(0) = – 1 y - y = e -* with y(0) =…

A: Take the Laplace transform on both sides of the equation.

Q: Solve the following DE using laplace transform method  y"-4y=0 when y(0)=0, y'(0)=6

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Q: Given the differential equation y'' - 3y' - 4y = 0, y(0) = 2, y'(0) = -1 Apply the Laplace Transform…

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Q: Find y as a function of a if 2'y" + 6zy/ - 36y = 0, %3D y(1) = 1, y(1) = 5. %3D y =

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Q: 330-5x²+0-5 Find c if it Gj is tangent for inx=1

A: The given equation of the curve is  y=0.5x2+0.5 To find the c is i + cj is tangent for y' at x = 1.

Q: 3) Is the function y(t)=cos(x(t)) linear or not?

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Q: Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below.…

A: Given initial value problem

Q: •T/4 t4 tant dt 2 + cos t -T/4

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Q: ý + 16y = 8 (t – ) sin (2t), y(0) = 0, ÿ(0) = 0

A: The solution is given by using some formulas of Laplace transform as follows :

Q: Consider the following initial-value problem. y' - y = 2 cos(3t), y(0) = 0 Find L{f(t)} for f(t) = 2…

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Q: 3- Solve D.E: * (Y +y = x* y") 3- By Bernoulli equation solve

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: The general solution of the 1st-order ODE, y' x² = Select one: a. y(x) = 2xx C+x b. y(x) = 2x -2² Cx…

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Q: Consider the following initial-value problem. y' y = 2 cos(4t), y(0) = 0 Find L{f(t)} for f(t) = 2…

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Q: dy = e*; y(0) = 2, using the method by Laplace transform. Solve Ans. et +1

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