Past exam of the physics 2 paper of the University of Oxford / 2014 / 9 / ii / Solution

The constant particular solution is $A=V/(4R)$, and the homogeneous equation has decay rate $2R/L$. Imposing $I_1(0)=0$ givesAs a separate check, the Thévenin equivalent seen by $L$ has open-circuit voltage $V/2$ and resistance $R+(2R\parallel 2R)=2R$, again giving $\tau =L/(2R)$.