Question 4 a) Find the solution of the following initial value problem by using method of Laplace transform. d'y_9y= 4e*: y(0) = 0, y'(0) =-1 dr? b) Besides Laplace transform, state two methods that can be used to solve the differential equation.

Q: Once again, we will only be completing step 1 and step 2. Given the differential equation y'" – 4y'…

A: Laplace transform of the function

Q: Question 13. A rabbit weighs 4 pounds at birth and 7 pounds two months later. The rabbit gains…

A:

Q: 1. The point (0,1) is intersect point of the differential equation (2x – 3y – 1)dx – [6(2x - 3y) –…

A: (2x-3y-1)dx-(6(2x-3y)-1)dy=0dydx=6(2x-3y)-1(2x-3y)-1 let…

Q: Question 4 Use Laplace transformation method to solve the differential equation y"-3y' + 2y = e2t…

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Q: x²y" + xy' + y = In x

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Q: 1. Consider the separable differential equation y' = x²y³. a. Plot the slope field of this…

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Q: Question 2 Find two linearly independent series solutions of the differential equa- tion y"-ry-2y =…

A: Given: y"-xy'-2y=0             1 Let y=∑n=0∞anxn be solution of (1)…

Q: 1. State the order of the given ordinary differential equation. Determine whether the equation is…

A: Given: sinθy''' -cosθy' = 2 To state: The order of the given differential equation and to determine…

Q: Solve the differential equation xyª) +6 y" = 0. ,(4) First convert this equation to a Cauchy-Euler…

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Q: Question 1 Question 2 Using variation of parameters which one of the The Laplace transform of…

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Q: Question 4.) Consider the differential equation y"+9y' +8y = 0 subject to the boundary conditions…

A: Laplace Transform of Derivatives For first-order derivative:L{f′(t)} =sL{f(t)}−f(0) For second-order…

Q: Give the differential equations for the Malthus model and the Verhulst model. Give a graphical…

A: The differential equations for the Malthus model and the Verhulst model. Give a graphical…

Q: The results of an initial valued problem of a differential equation is a family of curves. (A) True…

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Q: The equation, sin y-2 sin(2) sin(2y) y+ cos z + 2acos () cos(2y) = 0 is an exact differential…

A: We have to solve

Q: (a) A second-order differential equation is expressed by: у" — Зу' + 2у %3 е3t Solve this equation…

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Q: Question3: Solve the differential equation using the Laplace transform y" + 3y' – 4y = cos(2t); y(0)…

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Q: State the order of the given ordinary differential equation. (sin 8)y"" - (cos 8)y' = 2 Determine…

A: Part 1: Given the ordinary differential equation,                                               (sin…

Q: decide if the given statement is true or false,and give a brief justification for your answer.If…

A: The given statement is " The Laplace transform method for solving an initial value problem can also…

Q: b. Solve differential equation, subject to initial conditions y" - 9sin 3x – 2 sin x-1; y(0)=3; y 0)…

A: An ordinary differential equation is an equation containing independent variables, dependent…

Q: 2.1 By applying Newton's second law to a body at a certain distance x at time t, the following…

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Q: The solution of the differential equation given by x¨ − x = sinht, with x (0) = 0 and x˙ (0) = 0, it…

A: x-x = sin h r⇒ x-x = er-er2       ------ *au xi lasy equn of - *,         m2-1=0…

Q: Example 15 : Form the differential equation by eliminating the arbitrary constant from x tan =C.

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Q: 15. Use differentials to approximate V143.7

A: Use of differential

Q: In Problems : given initial-value problem. use the Laplace transform to solve the 34. y' – y = 2 cos…

A: let L{y}=Y(s)we knowL{y'}=sY(s)-y(0)L{cos at}=ss2+a2L{sin at}=1s2+a2L{eat}=1s-a

Q: By taking the Laplace transform of the differential equation initial condition is x (0)=0. If you…

A: I have solved using two methods

Q: can the differential equation be solved using the Laplace Transform? A=3 please quickly

A: To solve the given initial value problem using Laplace transformation: x''t−3x't+2xt=3e2t,…

Q: Question3:Solve the differential equation using the Laplace transform y" + 3y' – 4y = cos(2t); y(0)…

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Q: 1. The linear differential equation dx has the integrating factor equal to (Note: Simplify or solve…

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Q: Ye = e-4t [C, cos(t) + C2 sin(t)I

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Q: The equation, sin y- 2 sin(2) sin(2y) y+ cos z+2xcos (z) cos(2y) = 0 is an exact differential…

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Q: Question 5 Use variation of parameters to solve the differential equation x²y" + y = x. [Leave ₁ and…

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Q: Consider the following differential equation and initial value. У'%3D 2х — Зу + 1, У(1) %3D 6;…

A: We use the Euler's method, yn+1=yn+hf(xn, yn) to solve the given differential equation. Thus, we…

Q: Question 4 Given a second order differential equation d²x dx 2 + 10x = e²t dt² dt dx where t = 0, x…

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Q: Solve the given differential equation by finding, as in Example 4 from Section 2.4, an appropriate…

A: Here we need to solve the given differential equation.

Q: Basides laplace transform , state two methodes that can be used to solve the differential equation…

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Q: Solve the given differential equation by finding, as in Example 4 from Section 2.4, an appropriate…

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Q: Example 10: Form the partial differential equation by eliminating the arbitrary constan a and b…

A: We can find the answer as below

Q: To use the Laplace transform to solve the given initial value problem, we first take the transform…

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Q: 5.(i) Solve the differential equation (Dª – 1)y = 2 cos² x (ii) Find the Laplace transform of L[e 2t…

A: Part(i):   The general solutions of the nonhomogeneous equation is follows as y = yc + yp   The…

Q: State the order of the given ordinary differential equation. Determine whether the equation is…

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Q: 4. a) Transform the following Cauchy Euler equationto a differential with constant coefficients by…

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Q: Question 2 a) Use Laplace Transform to solve the differential equations given the initial condition…

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Q: QUESTION 4 Given f(x) = 8x³ + 2x. Estimate the value of ƒ(2.01) using differential. %3D

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Q: ŷ +zy = %3D yo)%=6

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Q: dx I+ ylz

A: An equation which involves the derivative or differential coefficient is called differential…

Q: Solve the given differential equation by finding, as in Example 4 of Section 2.4, an appropriate…

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Q: A (플) n (2프) %3D Cos dt?

A: This is the problem of differential equation.

Q: 4. When solving a differential equation using the Laplace transform, you apply the Laplace transform…

A: We use Laplace transform formula to find Y(s).

Q: 1. Discuss or show the methods in solving Exact and Non-Exact Differential Equations.

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Q: A direction field for the differential equation y' = cos(y) – sin(x) is given %3D below. a) Sketch…

A: Introduction: Every first-order ordinary differential equation has a slope field. The slope field is…