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Mathematics LibreTexts

4: Second-Order ODEs with Constant Coefficients

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The general linear second-order differential equation with independent variable t and dependent variable x=x(t) is given by ..x+p(t).x+q(t)x=g(t),

where we have used the standard physics notation .x=dx/dt and ..x=d2x/dt2. A unique solution of (???) requires initial values x(t0)=x0 and .x(t0)=u0. The equation with constant coefficients—on which we will devote considerable effort— assumes that p(t) and q(t) are constants, independent of time. The second-order linear ode is said to be homogeneous if g(t)=0.


This page titled 4: Second-Order ODEs with Constant Coefficients is shared under a CC BY 3.0 license and was authored, remixed, and/or curated by Jeffrey R. Chasnov via source content that was edited to the style and standards of the LibreTexts platform.

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