QUESTION 2 Solve the following differential equation with initial condition by using the Laplace transform method d²y dt² dy -4- dt y (0) = 3, - + 5y = = 2e¹ dy dt (0) = 1

Q: b) Solve the given system of differential equation by laplace transformation dx = x - y dt dy — 5х —…

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Q: dx3 dt3 + 4x = et; where d²x (0) dt² = dx(0) dt = x(0) = 0

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Q: Solve the differential equations by the method of Laplace transformation. 3y" – y' + 2y = 2x + 4

A: According to question given that :3y"-y'+2y=2x+4We have to calculate the Laplace transformation of…

Q: Solve the differential equation dx/dt-6x=3e6t under the initial condition x(0)=6-2 by using the…

A: The solution is given as

Q: dy dx = exy through (0,0)

A: A differential equation dydx=exy through (0,0). To Find: Slope field and also sketch the solution…

Q: 2y" – 2y' + 2y = -cos(3t), y(0) = 0, y'(0) = 1 6.

A: Given differential equation is 2y''-2y'+2y=-cos(3t)                  (1) y(0)=0, y'(0)=1 Let the…

Q: the fractal differential equation Day + =1/12 and y(0) = 1, Using Laplace transfo

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Q: Solve the differential equation dt - 8x 3e8t under the initial condition x(0) = 6 by using the…

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Q: A particular antibiotic is introduced to a petri dish containing 1000 newly discovered flesh -…

A: Let N0  be initial and Nt after t hours Then Nt = N0 (1 - 1/3)t.               Nt = N0…

Q: find the solution of following differential equation using Laplace transformation. y" + 3y + 2y = ex…

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Q: Transform (x + 3y)dr – xdy = 0 to a possible standard form of first ordered linear differential…

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Q: Example: Show that the functions: x=- - sinh and y: sinh- V3 3 dy dx dy ii ) dt dx Taken together…

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Q: Find the solution of following ODE by Laplace transform of the function x( t) and Ca(t) that…

A: According to guidelines we can solve only one problem

Q: 2- Solve the fractal differential equation Day + y = 5e²x With a = a = and and y(0) = 1, Using…

A: Given Fractal Differential Equation:  Where ​ and .Objective: To solve the given fractal…

Q: y - 5y + 6y = e2t

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Q: dx Use the Laplace transform to solve the given system of differential equations. =x-2y dt dy dt…

A: Using Laplace transform, we can solve the given problem.

Q: (b) Use the Laplace transform method to find the solution of d²y 6+9y= 4e", yo = 2, y1 = 0. dt dy…

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: Solve (D5 – D4 + 4D³ – 4D²) y = 32 cos (2x) – 20e *

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Q: Convert the differential equation d²y - 3y + 2y = 4 sin x dx² dx with the initial conditions y(0) =…

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Q: Count all the incidences in S4, a four-dimensional projective space of order q. That is, determine…

A: Ans-In a projective space of order $q$, there are $q^2 + q + 1$ points on a hyperplane, and $q^3 +…

Q: A dynamic system is described with the following differential equation: *+4x+20x = f(t), x(0)=1,…

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Q: Using the Laplace transform method, solve for t > 0 the following differential equation: d²x dx +3-…

A: The solution is given as

Q: a'1 = 3x1 – 3x2 + 2 a'2 = -6x1 – t X1 (0) = 1 X2 (0) = –1 %3D

A: Please check further steps for solution.

Q: The direction field for the differential equation dy = e*-y dx passes through the point y(-1) = 2 is…

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Q: lution of the logistic differential equation: dy dt alysis (and possibly a computer generated slope…

A: We have to find the solution of the given differential equation

Q: Consider an initial value problem given a linear differential equation of the form t20 with d'u d?u…

A: The given differential equation is: d3udt3+2d2udt2+dudt=3t2-2e-t ;       u(0)=u'(0)=u''(0)=0