Consider a series circuit consisting of a resistor of $R$ ohms, an inductor of $L$ henries, and variable voltage source of $V(t)$ volts (time $t$ in seconds). The current through the circuit $I(t)$ (in amperes) satisfies the differential equation: $$\frac{dI}{dt} + \frac{R}{L} I = \frac{1}{L} V(t)$$ Find the solution to this equation with the initial condition $I(0) = 0$, assuming that $R = 70 \, \Omega$, $L = 5$ H, and $V(t)$ is constant with $V(t) = 10$ V.

$I(t) =$