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Linear differential equations with constant coefficients

  • Bethany Fralick (a1) and Reginald Koo (a1)

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We consider the second order homogeneous linear differential equation (H)

$${ ay'' + by' + cy = 0 }$$
with real coefficients a, b, c, and a ≠ 0. The function y = emx is a solution if, and only if, m satisfies the auxiliary equation am2 + bm + c = 0. When the roots of this are the complex conjugates m = p ± iq, then y = e(p ± iq)x are complex solutions of (H). Nevertheless, real solutions are given by y = c1epx cos qx + c2epx sin qx.

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1.Plumpton, C. and Tomkys, W. A.: Sixth form pure mathematics, Volume two, Pergamon Press (1963).

Linear differential equations with constant coefficients

  • Bethany Fralick (a1) and Reginald Koo (a1)

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