EXERCISES 4.8 In Problems 1-20 solve the given system of differential equations by systematic elimination. 1. \frac{dx}{dt} = 2x - y \frac{dy}{dt} = x 2. \frac{dx}{dt} = 4x + 7y \frac{dy}{dt} = x - 2y 3. \frac{dx}{dt} = -y + t \frac{dy}{dt} = x - t 4. \frac{dx}{dt} - 4y = 1 \frac{dy}{dt} + x = 2 Answers to selected odd-numbered problems begin on page ANS-6. 5. $(D^2 + 5)x - 2y = 0$ $-2x + (D^2 + 2)y = 0$ 6. $(D + 1)x + (D - 1)y = 2$ $3x + (D + 2)y = -1$ 7. \frac{d^2x}{dt^2} = 4y + e^t \frac{d^2y}{dt^2} = 4x - e^t 8. \frac{d^2x}{dt^2} + \frac{dy}{dt} = -5x \frac{dx}{dt} + \frac{dy}{dt} = -x + 4y 9. $Dx + D^2y = e^t$ $(D + 1)x + (D - 1)y = 4e^t$
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dx/dt = m^2x - y^2 = 4x + 7y dy/dt = x = x - 2y To solve this system of differential equations by systematic elimination, we can start by eliminating one variable at a time. Step 1: Eliminate x from the second equation. dy/dt = x - 2y x = dy/dt + Show more…
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In Problems 1–20 solve the given system of differential equations by systematic elimination.
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