- #1
Rome_Leader
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Homework Statement
I have a circuit with input source x(t), which contains also an inductor and a capacitor in series which I have found to be related to the output voltage y(t) (across the capacitor) like so: LC*d2y/dt2 + y(t) = x(t). I have also found its roots through the quadratic equation to be complex, and equal to +/- the imaginary unit j.
The question asks me to show its homogenous solution has the form K1ej*a*t + K2ej*b*t, where a and b are the roots I found above.
Homework Equations
Unsure. See above for my progress so far.
The Attempt at a Solution
My solution has led me here, having gotten the above equation and its roots. I just do not know how to show that I can express the solution to the differential equation in the requested form. Any help would be greatly appreciated!