The following equation was derived from a RLC circuit:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\frac{d^2}{dt^2} (V(t)) + 6 \frac{d}{dt} (V(t)) + 5V(t) = 40[/tex]

Setting up the equation:

[tex]s^2 +6s + 5 = 0[/tex]

yields [tex]s = -1[/tex] and [tex]s = -5[/tex]

Giving me the general equation:

[tex]V(t) = k_{1}e^{-t} + k_{2}e^{-5t}[/tex]

But the general equation shown in the solution is:

[tex]V(t) = k_{1}e^{-t} + k_{2}e^{-5t} + k_{3}[/tex]

It's been a little while since my differential equations class and I'm not sure where the k3 comes from. Is it because the equation is nonhomogeneous and if that's the case will all second order nonhomogeneous equations that equal a constant have similar general equations?

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# Homework Help: Second Order Nonhomogeneous

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