1. The problem statement, all variables and given/known data Find a differential equation that describes the circuit that includes only vin and vout as variables. 2. Relevant equations C(dvin - dvout)/dt = i vin - vout = L(di/dt) 3. The attempt at a solution So the answer I got was: C(d2vout/dt2) + vout = LC(d2vin/dt2) My question is, is it allowable to break up the capacitor derivate like that? After substituting in for i, I got: vout = Ld/dt(C(dvin - dvout)/dt) Then I broke up the capacitor into vin and vout terms and just rearranged. But I'm not 100% sure if that's legal.