Question

Solve the given system of differential equations by systematic elimination. 2 dx/dt - 6x + dy/dt = e^t dx/dt - x + dy/dt = 6e^t (x(t), y(t)) = (C1e^5t + 4/5e^t, 6e^t - 6/5C1e^5t + C2) Solve the given initial-value problem. dx/dt = y - 1 dy/dt = -6x + 2y x(0) = 0, y(0) = 0 x(t) = 1/3(e^t(-cos sqrt(5) t + 1/sqrt(5)sin sqrt(5) t) + 1) y(t) = e^t(1/3(sqrt(5) + 1/sqrt(5))sin sqrt(5) t) + 1

          Solve the given system of differential equations by systematic elimination.
2 dx/dt - 6x + dy/dt = e^t
dx/dt - x + dy/dt = 6e^t
(x(t), y(t)) = (C1e^5t + 4/5e^t, 6e^t - 6/5C1e^5t + C2)
Solve the given initial-value problem.
dx/dt = y - 1
dy/dt = -6x + 2y
x(0) = 0, y(0) = 0
x(t) = 1/3(e^t(-cos sqrt(5) t + 1/sqrt(5)sin sqrt(5) t) + 1)
y(t) = e^t(1/3(sqrt(5) + 1/sqrt(5))sin sqrt(5) t) + 1

Solve the given system of differential equations by systematic elimination.
2 dx/dt - 6x + dy/dt = e^t
dx/dt - x + dy/dt = 6e^t
(x(t), y(t)) = (C1e^5t + 4/5e^t, 6e^t - 6/5C1e^5t + C2)
Solve the given initial-value problem.
dx/dt = y - 1
dy/dt = -6x + 2y
x(0) = 0, y(0) = 0
x(t) = 1/3(e^t(-cos sqrt(5) t + 1/sqrt(5)sin sqrt(5) t) + 1)
y(t) = e^t(1/3(sqrt(5) + 1/sqrt(5))sin sqrt(5) t) + 1

Added by Roger M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

08/12/2022

Step 1

Step 1:** Given system of differential equations: \[ \frac{dx}{dt} = 6x + ae^{t} \] \[ \frac{dy}{dt} = x + 6e^{t} \] ** Show more…

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Solve the given system of differential equations by systematic elimination. 2 dx/dt - 6x + dy/dt = e^t dx/dt - x + dy/dt = 6e^t (x(t), y(t)) = (C1e^5t + 4/5e^t, 6e^t - 6/5C1e^5t + C2) Solve the given initial-value problem. dx/dt = y - 1 dy/dt = -6x + 2y x(0) = 0, y(0) = 0 x(t) = 1/3(e^t(-cos sqrt(5) t + 1/sqrt(5)sin sqrt(5) t) + 1) y(t) = e^t(1/3(sqrt(5) + 1/sqrt(5))sin sqrt(5) t) + 1