Solve the given system of differential equations. ??/?? = ? + 4? ??/?? = ? +...

Solve the given system of differential equations. ??/?? = ? + 4? ??/?? = ? + y

Expert Solution

Colby Messinger answered 2 years ago

Please make sure you solve both correctly. 1) Solve the given system of differential equations by...

Please make sure you solve both correctly. 1) Solve the given system of differential equations by systematic elimination. (2D2 − D − 1)x − (2D + 1)y = 8 (D − 1)x + Dy = −8 ((x(t),y(t))= ? 2) Solve the given initial-value problem. dx dt = y − 1 dy dt = −7x + 2y x(0) = 0, y(0) = 0 x(t) = ? y(t)= ?

Solve the given system of differential equations by systematic elimination. (D2 − 1)x − y =...

Solve the given system of differential equations by systematic elimination. (D2 − 1)x − y = 0 (D − 1)x + Dy = 0 I had this as my answer and webassign rejected it: (x(t), y(t)) = c_1e^t+e^{-\left(\frac{t}{2}\right)}\left(c_2\cos \left(\frac{\sqrt{3}}{2}t\right)+c_3\sin \left(\frac{\sqrt{3}}{2}t\right)\right),e^{-\left(\frac{t}{2}\right)}\left(\left(-\frac{3}{2}c_2-\frac{3\sqrt{3}.}{4}c_3\right)\cos \left(\frac{\sqrt{3}}{2}t\right)+\left(\frac{-3}{2}c_3+\frac{3\sqrt{3}}{4}c_2\right)\sin \left(\frac{\sqrt{3}}{2}t\right)\right)

Solve the given system of differential equations by systematic elimination. (D + 1)x + (D −...

Solve the given system of differential equations by systematic elimination. (D + 1)x + (D − 1)y = 6 ; 7x + (D + 6)y = −1

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

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

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. (D − 1)x + (D2 +...

Solve the given system of differential equations by systematic elimination. (D − 1)x + (D2 + 1)y = 1 (D2 − 1)x + (D + 1)y = 2 (x(t), y(t)) =

Write the second order differential equation as a system of two linear differential equations then solve...

Write the second order differential equation as a system of two linear differential equations then solve it. y" + y' - 6y = e^-3t y(0) =0 y'(0)=0

Series Solutions of Ordinary Differential Equations For the following problems solve the given differential equation by...

Series Solutions of Ordinary Differential Equations For the following problems solve the given differential equation by means of a power series about the given point x0. Find the recurrence relation; also find the first four terms in each of two linearly independent solutions (unless the series terminates sooner). If possible, find the general term in each solution. (1-x)y"+xy-y=0, x0=0

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Solve the given system of differential equations. ??/?? = ? + 4? ??/?? = ? +...

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