1)What is the advantage of solving differential equations using Laplace Transforms over prior time-domain techniques cover...

1)What is the advantage of solving differential equations using Laplace Transforms over prior time-domain techniques cover thus far this semester (Chps 1-5)?

2) When using Laplace Transforms, what is the difference in the notation between lower case (i.e. f(t)) and upper case (i.e. F(s)) letters?

3) If the Laplace Transform is an integral as shown in Sec 7.1, pg 438, equation #1, how can Dr. Tran claim that the Laplace Transform technique does not require use of Calculus? Is he crazy? Please explain.

Expert Solution

Colby Messinger answered 2 years ago

Solving Differential Equations using Laplace Transform

Solving Differential Equations using Laplace Transform a) y" - y' -2y = 0 y(0) = 1, y'(0) = 0 answer: y = 1/3e^2t + 2/3e^-t b) y" + y = sin2t y(0) = 2, y'(0) = 1 answer: y(t) = 2cost + 5/3 sint - 1/3sin2t c) y^4 - y = 0 y(0) = 0, y'(0) = 1, y"(0) = 0, y'''(0) = 0 answer y(t) = (sinht + sint)/2

1. Use Laplace transforms to solve the following differential equations for ?(?) for ? ≥ 0....

1. Use Laplace transforms to solve the following differential equations for ?(?) for ? ≥ 0. Use ?(0) = 0 and ?̇(0) = 1 for each case. i. 0 = ?̈(?) + 2?̇(?) + 4?(?) ii. 0 = ?̈(?) + 3?̇(?) + 2?(?) iii. 5 = ?̈(?) + 5?̇(?) + 6?(?) 3. For the three differential equations from problem one determine the steady-state value of the system using: a. lim?→0 ??(?), b. lim ?→∞ ?(?) analytically, c. lim ?→∞ ?(?)...

3) Laplace Transform and Solving first order Linear Differential Equations with Applications The Laplace transform of...

3) Laplace Transform and Solving first order Linear Differential Equations with Applications The Laplace transform of a function, transform of a derivative, transform of the second derivative, transform of an integral, table of Laplace transform for simple functions, the inverse Laplace transform, solving first order linear differential equations by the Laplace transform Applications: a)))))) Series RL circuit with ac source [electronics]

4) Laplace Transform and Solving second order Linear Differential Equations with Applications The Laplace transform of...

4) Laplace Transform and Solving second order Linear Differential Equations with Applications The Laplace transform of a function, transform of a derivative, transform of the second derivative, transform of an integral, table of Laplace transform for simple functions, the inverse Laplace transform, solving first order linear differential equations by the Laplace transform Applications: a) Series RLC circuit with dc source b) Damped motion of an object in a fluid [mechanical, electromechanical] c) Forced Oscillations [mechanical, electromechanical] You should build the...

In Exercises 5–37, solve the given differential equations by Laplace transforms. The function is subject to...

In Exercises 5–37, solve the given differential equations by Laplace transforms. The function is subject to the given conditions. 13. 4y″ + 4y′ + 5y = 0, y(0) = 1, y′(0) = -1/2 17. y″ + y = 1, y(0) = 1, y′(0) = 1

Explain the process of using Laplace transforms for solving a difference equation with an initial condition....

Explain the process of using Laplace transforms for solving a difference equation with an initial condition. You may illustrate with an example, but you don’t have to solve the whole thing out.

write the theory and formulas for solving the systems of equations using the Laplace transform. Must...

write the theory and formulas for solving the systems of equations using the Laplace transform. Must contain bibliography

3. Solve the following differential equations by using LaPlace transformation: 2x'' + 7x' + 3x =...

3. Solve the following differential equations by using LaPlace transformation: 2x'' + 7x' + 3x = 0; x(0) = 3, x'(0) = 0 x' + 2x = ?(t); x(0-) = 0 where ?(t) is a unit impulse input given in the LaPlace transform table.

1. Why guessing and checking is alright in solving differential equations In lecture (and possibly in...

1. Why guessing and checking is alright in solving differential equations In lecture (and possibly in other courses), you have seen differential equations solved by looking at the equation, moving parts around, reasoning about it using an analogy with eigenvalue/eigenspaces, and then seeing that the solution that we proposed actually works — i.e. satisfies all the conditions of the differential equation problem. This process should have felt a bit different than how you have seen how systems of linear equations...

what will be transient telegrapher's equation solution using laplace transforms if R,G parameter is not zero....

what will be transient telegrapher's equation solution using laplace transforms if R,G parameter is not zero. Where R= RESISTOR OF WIRE AND G= conductance between line.

Question