Use Laplace transformations to solve the following ODE for x(t): x¨(t) + 2x(t) = u˙(t) +...

Use Laplace transformations to solve the following ODE for x(t):

x¨(t) + 2x(t) = u˙(t) + 3u(t)

u(t) = e^−t

Initial conditions

x(0) = 1, x˙(0) = 0, u(0) = 0

Expert Solution

Colby Messinger answered 2 years ago

Use Laplace transformations to solve the following differential equations: dy(t)/dt + a y(t) = b; I.C.s...

Use Laplace transformations to solve the following differential equations: dy(t)/dt + a y(t) = b; I.C.s y(0) = c d2y(t)/dt2 + 6 dy(t)/dt + 9 y(t) = 0; I.C.s y(0) = 2, dy(0)/dt = 1 d2y(t)/dt2 + 4 dy(t)/dt + 8 y(t) = 0; I.C.s y(0) = 2, dy(0)/dt = 1 d2y(t)/dt2 + 2 dy(t)/dt + y(t) = 3e-2t; I.C.s y(0) = 1, dy(0)/dt = 1

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

Solve the following initial value problem ut + 2ux − 2u = e t+2x , u(x,...

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Use Laplace transforms to solve x''− 7x' + 6x = e^t + δ(t − 2) +...

Use Laplace transforms to solve x''− 7x' + 6x = e^t + δ(t − 2) + δ(t − 4), x(0) = 0, x'(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

Solve the differential equation. x''(t)+2x'(t)+5x(t) = 2

Find the Laplace transform of the following functions: a. p(t) = 6[u(t − 2) − u(t...

Find the Laplace transform of the following functions: a. p(t) = 6[u(t − 2) − u(t − 4)] b. g(t) = (4 + 3e−2t)u(t) c. h(t) = 2r(t) − 2r(t − 2)

Solve this Initial Value Problem using the Laplace transform. x''(t) + 6 x'(t) + 25x(t) =...

Solve this Initial Value Problem using the Laplace transform. x''(t) + 6 x'(t) + 25x(t) = cos(t), x(0) = 0, x'(0) = 1

Please solve the following: ut=uxx, 0<x<1, t>0 u(0,t)=0, u(1,t)=A, t>0 u(x,0)=cosx, 0<x<1

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