determine the characteristic equation for the current through the capacitor (iC), the current through the inductor (iL) and the current through the resistor (iR).

I have my answer, but I'm not sure if its accurate or not, or if I have answered the question that is being asked. My attempt is in the reply thread. Please help me Thank you

I have my answer, but I'm not sure if its accurate or not, or if I have answered the question that is being asked. My attempt is in the reply thread. Please help me Thank you
