Solve the given DE using the Laplace Transform Method. Use the formulas and properties taught in class. y" – 4y' – 5y = g (t) ; y (0) = 2 , y' (0) = 5 %3D g(t) = {2". t,0 1

Q: Q2: Find The Fourier cosine and transform of the following functions: SSint, ostse (1) f(t) = 10₂…

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

Q: Use the Laplace transform to solve the given initial-value problem. y' - y = 2 cos(9t), y(0) = 0…

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Q: Solve the IVP using Laplace transforms. x(0) = 4 15. x'(t) = t², %3D %3D

A: Here we will use Laplace transform method to solve the differential equation.

Q: 3. Suppose y(t) is the inverse Laplace transform of the following function: y(t) = L-1 What is lim…

A: We have to find the inverse Laplace transform of the given function.

Q: (c) S, y*/1- y² dy

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Q: Find dyldx for the following xVx² + 1 In y = ln (x + 1)3

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Q: Use the definition to find the Laplace Transform of the given function (t, 0st<1 f(t)= OSt<1 1, t21

A: The Laplace transform of the function f(t) is represented as F(s) or L[f(t)], it is defined as…

Q: t も c6 10. XCt)> { -8 + -8 t ct-6)? » t >6

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Q: Using convolution property of Laplace Transform, solve for y(t) of the following: 2) y(t) = sin(nt)…

A: The given problem is to solve for y(t) for the given function by using convolution property of…

Q: Find the Laplace transform F(s), given that f(t) is: (a) 2tu(t – 4) (b) 5 cos(t) 8(t – 2)

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Q: DEvaluate x²dx V2-X

A: Substitution method of Definite Integration : Suppose  and let  be continuous over an interval Let…

Q: Solve using Lapiace transform: P4t - uz = xt, t> 0, u(0, t) = 2, u(x, 0) = 1. = 2, u(x,0) = 1. %3D…

A: Introduction: Apart from solving ordinary differential equation with initial values, partial…

Q: Find the Laplace Transforms of the following functions: (c) f(t) = cos³ t. (e) f(t) = sin 2t cos 3t.

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Q: 4. Use the Laplace transform to solve the IVP a" + 4x' + 4x = 4e24, r(0) = 0, r' (0) = 1.

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Q: using Laplace transform, solve the equation below. y'' -2y' + 2y = cos (t)         y(0) = 1,  y'(0)…

A: To find the solution of differential equation we use the properties of Laplace transform of…

Q: 9. (Chapter 10, #20) Prove that for every n E N, (1+2+3+ · ..+n)2 = 13 + 23 + 33 + ...+ n³.

A: To prove the result ''∀n∈N,1+2+3+...+n2=13+23+33+...+n3'' by Mathematical induction: First prove for…

Q: 15. Solve the IVP using Laplace transforms. x'(t) = t?, x(0) = 4

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Q: (1 + xe* kty + (ye* + yxe* + 2)dx = 0

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Q: Find the Laplace transform of f(t), where ƒ(t) is f(t)=4e³ sint cost and f(t)=r’sinh2t .

A: We know that  Leat sin(bt) = b(s-a)2+b2. Now  Lf(t)=L4 e3t sint cost= 2 L e3t 2sint cost= 2 L{e3t…

Q: (D² + 2D- 3)y = sin 2x; y(0) = y'(0) = 0 (Use The Laplace Transform)

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Q: Use Laplace transforms to solve the following initial value problem. x''+x=sin 2t, x(0) = 0, x'(0) =…

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Q: The following is an IVP: Let's introduce Y(a) = C(v(t)) +4y= cos(2), v(0)=3, (0)-8. Part 1 Apply the…

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Q: Laplace transform

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Q: sen(22t) 0<t <- f(t) = cos(12t) t25

A: The given function: f(t)=sen(22t)   0≤t&lt;π2cos(12t)   t≥π2 To find the transforms of the function…

Q: 2Ct -4)4 fct) = 4. 2Ct -4) %3D

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