In Problems 1–20 solve the given system of differential equations by systematic elimination. 1. dx/dt = 2x - y dy/dt = x 2. dx/dt = 4x + 7y dy/dt = x - 2y 3. dx/dt = -y + t dy/dt = x - t 4. dx/dt - 4y = 1 dy/dt + x = 2 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. d^2x/dt^2 = 4y + e^t d^2y/dt^2 = 4x - e^t 8. d^2x/dt^2 + dy/dt = -5x dx/dt + dy/dt = -x + 4y 9. Dx + D^2y = e^3t (D + 1)x + (D - 1)y = 4e^3t 10. D^2x - Dy = t (D + 3)x + (D + 3)y = 2
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