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

Expert Solution

Here is an illustration of the method of solving linear systems using Laplace transforms :-

The rules of transformation are written in the following table --

Let us see an example,

BIBLIOGRAPHY :-

DIFFERENTIAL EQUATIONS by SHEPLEY L. ROSS, WILEY
LAPLACE TRANSFORMS by M. R. SPIEGEL, Mc Graw Hill

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

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...

Use laplace Transform in solving the ff.: After cooking for 45 minutes, when a cake is...

Use laplace Transform in solving the ff.: After cooking for 45 minutes, when a cake is removed from an oven its temperature is measured at 300°F. 3 minutes later its temperature is 200°F. The oven is pre heated, and so at t=0, the cake mixture is at the room temperature of 70°F. The temperature of the oven increases linearly until t=4 minutes, when the desired temperature of 300°F is attained; thereafter the oven temperature is constant 300°F for t is...

Use laplace transform in solving the ff.: After cooking for 45 minutes, when a cake is...

Use laplace transform in solving the ff.: After cooking for 45 minutes, when a cake is removed from an oven its temperature is measured at 300°F. 3 minutes later its temperature is 200°F. The oven is not preheated, so at t=0, when the cake mixture is placed into the oven, the temperature inside the oven is also 70°F. The temperature of the oven increases linearly until t=4 minutes, when the desired temperature of 300°F is attained; thereafter the oven temperature...

A system of differential equations solved by the Laplace transform has led to the following system:...

A system of differential equations solved by the Laplace transform has led to the following system: (s-3) X(s) +6Y(s) = 3/s X(s) + (s-8)Y(s) = 0 Obtain the subsidiary equations and then apply the inverse transform to determine x (1)

Solve the following constant coefficient linear differential equations using Laplace Transform (LT), Partial Fraction Expansion (PFE),...

Solve the following constant coefficient linear differential equations using Laplace Transform (LT), Partial Fraction Expansion (PFE), and Inverse Laplace Transform (ILT). You must check answers in the t-domain using the initial conditions. Note: Complex conjugate roots y ̈ (t) + 6 ̇y (t) + 13y (t) = 2 use the initial conditions y(0) = 3, ̇y(0) = 2.

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...

Use the Laplace transform to solve the given system of differential equations. d2x dt2 + 3...

Use the Laplace transform to solve the given system of differential equations. d2x dt2 + 3 dy dt + 3y = 0 d2x dt2 + 3y = te−t x(0) = 0, x'(0) = 4, y(0) = 0

Use the Laplace transform to solve the given system of differential equations. dx/dt + 3x +...

Use the Laplace transform to solve the given system of differential equations. dx/dt + 3x + dy/dt = 1 dx/dt − x + dy/dt − y = e^t x(0) = 0, y(0) = 0

Question