Chapter 8 - Linear Differential Equations of Order n - 8.6 RLC Circuits - Problems - Page 546: 6

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The behavior of an RLC circuit is: $\frac{dq^2}{dt^2}+\frac{R}{L}\frac{dq}{dt}+\frac{1}{LC}q=\frac{E}{L}$ Let $i=\frac{dq}{dt}$ Rewrite: $\frac{d}{dt}(\frac{d^2q}{dt^2})+\frac{R}{L}\frac{d^2q}{dt^2}+\frac{1}{LC}\frac{dq}{dt}=\frac{1}{L}\frac{dE}{dt}$ $\frac{d^2i}{dt^2}+\frac{R}{L}\frac{di}{dt}+\frac{1}{LC}i=\frac{1}{L}E\frac{dE}{dt}$