Find the Laplace transform of d2y/dt2

Find the Laplace transform of d²y/dt²

Expert Solution

Colby Messinger answered 2 years ago

Use Laplace transform method to solve the following initial value problems (a) d2y/dt2 + y =...

Use Laplace transform method to solve the following initial value problems (a) d2y/dt2 + y = e^ −t ; y(0) = 0, y′ (0) = 0. (b) d2y/dt2+ y = t subject to the initial conditions y(0) = 0, y′ (0) = 2 (c) dy/dt + 2y = 4e 3t subject to the initial condition y(0) = 1.

Solve the differential equation both by undetermined coefficients and the Laplace transform: d2y/dt2– 3 dy/dt +...

Solve the differential equation both by undetermined coefficients and the Laplace transform: d2y/dt2– 3 dy/dt + 2y = 6 exp(3t), y(0) = 6, y’(0) = 14.

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. 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 the Laplace transform to find the solution of the IVP: a.) 2y' + y =...

Use the Laplace transform to find the solution of the IVP: a.) 2y' + y = 1, y(0) = 2 (answer should be y(t) = 1 + e-t / 2 ) f.) 4y" + y = 0, y(0) = -1, y'(0) = -1 (answer should be y(t) = -sin(t) - cos(t)) Please show work!

Find the Laplace transform of the following functions. (a) f (t) = { 6 0 < ...

Find the Laplace transform of the following functions. (a) f (t) = { 6 0 < t ≤ 4 8 t ≥ 4 (b) f (t) = { t2 0 ≤ t < 3 0 t ≥ 3 (c) f (t) = { 0 0 ≤ t < π/4 cos[7(t − π/4)] t ≥ π/4

1. Find the solution by using the Laplace transform. a) y ′′ + 2ty′ −4y =...

1. Find the solution by using the Laplace transform. a) y ′′ + 2ty′ −4y = 1 , y(0) = y ′ (0) = 0

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...

Find the inverse Laplace transform for 1 / ((s^2+1)(s+1))

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