 Solution

Use positive current in the charging direction and passive voltage drops across $R,L,C$. The five ideal elements obeyThe battery maintains its emf independently of current. An ideal open switch has $I=0$ with its voltage unconstrained; an ideal closed switch has $v_{\mathrm{switch}}=0$ with its current unconstrained. These statements are the switch's piecewise current-voltage relation. Inductor current continuity and capacitor-voltage continuity hold when no impulse voltage or current is imposed.