Use the variation of parameters to find the general solution of the following ODE. z'' + z = tan2 x

Q: 3 Solve the following equations by Laplace transforms. dx (a) +3x =e-2t dt given that x =2 when t 0…

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Q: Suppose solving an equation by Laplace transform results in Y(s) = s2 + 64' Evaluate y(7).

A: We have to solve given problem:

Q: Find the value of the summation. cos(Tk) = k=0

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Q: (xy^2+y)dx -xdy =0

A: Given: (xy2+y)dx-x dy=0

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

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Q: What technique should you use to solve the ODE that arises from the Euler's equation associated with…

A: A multivariable function f(x,y) is a rule that is used to associate a number or quantity with a…

Q: tody + y² = 0 dt

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Q: Use Euler’s explicit method to solve the ODE dy/dx= -1.4 + 8e^ -0.3x from x= 0 to x= 2.4 with the…

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Q: Solve the given IVP using Laplace Transforms. Solve for x(s) and STOP! (Express x(s) as a single…

A: Given IVP is x'' + 9x = cos3t,  x0=0,  x'0=2

Q: +3Y=e

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Q: Consider the following first-order ODE where y is the dependent variable and x is the independent…

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Q: Identify the Bernoulli's equation of first order ODE. None of these b. dy -+10x²y=sin x dx C. dy…

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Q: The equation implicitly defines as a function of t. Find dr dt da dt 11 2 cos (6 x) = -8

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Q: Solve the ODE using the Laplace Transform method: x" + 4x = 1+t; x(0) = 0, x'(0) = 2

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Q: 2. y" – 2y' = -4 y(0) = 0,y'(0) = 4

A: For the solution of an initial value problem where boundary conditions are available, take the…

Q: Solve the following equation using Laplace transform: y' + y - sin 3t dr = 0 %3D *Note: Assume…

A: Given equation is y'+y−∫0tsin3τdτ=0......(1) First of all solve ∫0tsin3τdτ…

Q: Solve the following equations by Laplace transforms. (b) 3x - 6x = sin 2t given that x =1 when t = 0

A: To find the Laplace transform of the given differential equation, first we take the Laplace…

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

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Q: Solve the following equations by Laplace transforms. dx (a) +3x =e-2t given that x = 2 when t = 0 dt

A: Since every part is independent of each other so according to the guideline , I am going to solve…

Q: Classify the following ODE and solve the initial value problem y(1-x2)y' = xy2 - cosx.sinx , y(0)=2

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Q: Using Laplace Transform, solve the following initial value problem 3y' - 4y = sin 2t y(0) = ;

A: Given: 3y'-4y=sin2t  ; y0=13   Use the Laplace transform of derivation of function,…

Q: 1. Use the Euler, methods to solve the following ODES : improved Euler and Runge-kutta dy = x (1+ x)…

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Q: Consider the following first-order ODE: (2xy – sec? x)dx + (x² + 2y)dy = 0 || Solve it using the…

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Q: Find the solution to the ODE below using Laplace Transform: y' +y = e-3t y(0) = 0

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Q: Solve for the Laplace transform of e2t sint cost cos 2t cos 4t 1 s-4s+20 s-4s+68 -4s+20

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Q: Consider the following ODE d^2y/dx^2+x^2dy/dx-cos(x)y=y-2xy With initial conditions: y(0)=3 and…

A: Step:-1 Given that   d2ydx2 +x2dydx -cosx y =y-2xy⇒y'' +x2 y' -cosx y =y-2xy ---(1) with initial…

Q: Solve the following equations by Laplace transforms (b) 3 dx/dt – 6x = sin 2t given that x= 1 when…

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Q: 3) Find the general solutions only of the following higher order ODE by method of undetermined…

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Q: 5. Solve the given ODE using the method of undetermined coefficients. y" − 4y = x² + 4x − 3 -

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Q: Use Euler's method to solve the following ODES wwwwwwww dy dx = -2y + 4e¯*, with h = 0.18 from x = 0…

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Q: y = sin 3t dt – y

A: Calculated integration and the applied laplace transformation in both sides

Q: Solve each of the following by Laplace Transform: 1.) +2. +y=sinh 3t — 5 cosh3t ; y (0) =−2 , ý (0)…

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Q: solve the following equation using laplace transforms: note:= 1 not 11 dx - 3 dx + 2x = 0, x(0) = 0,…

A: Given d2xdt2 -3dxdt + 2x = 0                                    (1)x(0) = 0…

Q: Solve the following DE using Laplace Transform: 2. y" – 2y' = -4 y(0) = 0, y'(0) = 4

A: The solution is given as

Q: y" - 2 y' + 2y = 4 cos 2t + 2 sin 2t , y (0) = 1 , y' (0) = 1 %3D

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Q: Solve the ODE using Galerkin method for two equal length elements d²U + 2 = 0, 0< x< 3 dx2 if u(0) =…

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Q: Solve the following equation using Laplace transform: y = sin 3t dt – y' *Note: Assume initial…

A: We are given : y=∫0tsin3τdτ -y'⇒y+y'=∫0tsin3τdτ⇒y+y'=-cos (3τ)30t⇒y+y'=-13cos 3t -1 Taking Laplace…

Q: Solve the following IVP using Laplace Transform: 2. y" – y = 4 cost y(0) = 0 y'(0) = 1

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Q: 1 Let J = dx. The substitution x = tan(0) transforms the x2 V9x2 + 1

A: Given,            J=∫1x29x2+1dxTo find: The substitution x=13tanθ transforms then integral J into.

Q: Solve the following ODE using Laplace Transforms Method: y'+y=2sinx when y(0) = -1

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Q: 1. Solve the following ODE using separable variable method: dy +(x+2)y³ =0. dx а)

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Prove by conventional integration that the Laplace transform of the given function is equal to the…

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Q: Solve for x(t) for the given ODE with initial values. x"(t) + 0.25x(t) = 0 with x(0)=3 and x'(0)-4

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Q: Solve the following IVP using Laplace Transform.…

A: We have to solve given IVP using Laplace transform.

Q: 3 y" + 9y = sen2t, 2

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Q: Use Laplace transform to the following (so called integro-differential equation) to find y(t) '() =…

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Q: Find F'(x) given that F(x) 3+sin (5t) dt. |3D In (t8) Provide your answer below: F'(x) =

A: The objective is to find F'(x).

Q: 3 Solve the following equations by Laplace transforms. dx (a) + 3x = e-2t given that x = 2 when t =…

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Q: - y' + y = 2 sinx when y(0) = -1

A: As per the company guidelines We can first question only. Please understand. Kindly repost the…

Q: 10. Solve the following ODES by separating variables (a) dx Cos 5t where x(0) = 1 dt x2 (Ъ) dy e2y+t…

A: Given: (a) dxdt=cos5tx2 where x0=1  (b) dydt=e2y+t To determine: The solution of given ODEs by…