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

Expert Solution

Colby Messinger answered 2 years ago

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

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

Solve the given system of differential equations by systematic elimination. 2 dx dt − 6x +...

Solve the given system of differential equations by systematic elimination. 2 dx dt − 6x + dy dt = et dx dt − x + dy dt = 3et

2) Solve the system of equations below dx/dt – 3x – 6y = t^2 ...

2) Solve the system of equations below dx/dt – 3x – 6y = t^2 dx/dt + dy/dt – 3y = e^t

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)

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

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

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.

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.

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