# Unit II: Second Order Constant Coefficient Linear Equations

Unit Introduction

The general solution to second order differential equations with constant coefficients is:

{$$ x = x_h + x_{p^\prime} $$}

where {$ x_h $} is the solution to the homogeneous equation of the form:

{$$ ax^{\prime\prime} + bx^{\prime} + cx = 0 $$}

and {$ x_p $} is the particular solution to the inhomogeneous equation

{$$ ax^{\prime\prime} + bx^{\prime} + cx = f(t) $$}.

{$ f(t) $} is called the forcing term or input, and special consideration is given to the cases in which it is sinusoidal, {$ f(t) = B \cos \omega t $}.

<< MIT 1803 SC Differential Equations Unit 1 N | Trail MIT 18.03SC Differential Equations | Modes and the Characteristic Equation >>

*Sources:*

- Periodic response of a second order system. Modeled on the MIT mathlet
*Amplitude and Phase: Second Order I.*

*Recommended:*

** Categories:** Differential Equations Second Order Differential Equations

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