Engineering Figuring Out a General Solution for RLC Series Circuit

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The discussion focuses on finding a general solution for the differential equation dI/dt in an RLC series circuit. The user is seeking feedback on their work, indicating that the resulting waveform is incorrect. A key error identified is the improper use of the quadratic formula, specifically neglecting to square the resistance coefficient R under the radical. Participants are encouraged to review the user's calculations for additional mistakes. Clarifying these errors is essential for achieving an accurate solution for the RLC circuit.
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So, I have been trying to come up with a general solution for dI/dt in an RLC circuit.

I have attached the work I have done so far. I don't know where but I am making a mistake and the waveform is not coming out right. Would really appreciate a look over my work to see if I made any obvious errors.
 

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You did not use the quadratic formula properly. You forgot to square the coefficient R under the radical.
 

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