Use Laplace transforms to solve the following system of diﬀerential equations.

Expert Solution

in question there is no given differential equation to do laplace transform.

so i took a example and apply laplace transform on that and provide to u for reference.

in this images i have done only laplace transform and to find the complete y(t)

follow this after apply inverse laplace transform...

comment me if u need more information on laplace transformations on differential equations

milcah answered 2 years ago

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 ?→∞ ?(?)...

Use Laplace transforms to solve the system. x' - 5x - 4y = 0 x(0) =...

Use Laplace transforms to solve the system. x' - 5x - 4y = 0 x(0) = 1 y' + x - y = 0 y(0) = -1

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

Use Laplace transforms to solve the following initial value problem : y'' - 3y' +2y =...

Use Laplace transforms to solve the following initial value problem : y'' - 3y' +2y = 1 + cos (t) + et , y(0) =1, y' (0) = 0

Use laplace transforms to solve the following problem. y' + 20y = 6sin 2x; y(0) =...

Use laplace transforms to solve the following problem. y' + 20y = 6sin 2x; y(0) = 6

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

Use the Laplace transform to solve the given system of differential equations. d2x/dt2 + x −...

Use the Laplace transform to solve the given system of differential equations. d2x/dt2 + x − y = 0 d2y/dt2 + y − x = 0 x(0) = 0, x'(0) = −4 y(0) = 0, y'(0) = 1

Use Laplace transforms to solve the initial value problem: x' = 2x + y, y' =...

Use Laplace transforms to solve the initial value problem: x' = 2x + y, y' = 6x + 3y; x(0) = 1, y(0) = -2

Use the Laplace transform to solve the given system of differential equations. dx/dt + 2x +dy/dt=...

Use the Laplace transform to solve the given system of differential equations. dx/dt + 2x +dy/dt= 1 dx/dt− x+ dy/dt− y= e^t x(0) = 0, y(0) = 0

Question