Consider a parallel RL-circuit, connected to a current source $I(t)$. The signal is for the moment arbitrary, so not sinusoidal.
QUESTION 1: Find the differential equation of the voltage $U(t)$.
In the case of a RL (or RLC) circuit in series one would write: $$ U(t) = \frac{1}{C}\int{I(t)dt}+L\frac{dI(t)}{dt}+RI(t) $$ In parallel - in our case - one can write: $$ I(t) = \frac{1}{R}U(t)+\frac{1}{L}\int{U(t)dt} $$ but I don't know how to express $U(t)$.
QUESTION 2: Calculate $U(t)$ for
$$ I(t) = \begin{cases} 0 & t<0\\ I_0 & t\geq 0\\ \end{cases} $$
How would I approach these two questions?