di/dt for R of general RLC, KCL dt algebra
At t = 0+ the dominant component is the capacitor C1. Its effect trumps any effects from R1 and super-trumps any effect from L1 in series with R2. So, at t = 0+ C1 acts like a short circuit and starts to charge up taking all the 4 amps from the current source. Given this: -

$$i_c = C\cdot \frac{dv}{dt}$$

We can say that the initial rate of change of voltage is \$\frac{4}{0.25}\$ volts per second (16 volts per second) hence, the initial rate of change of current through R1 is 4 amps per second.

After everything has settled down and in the fullness of time C1 acts like an open circuit and L1 acts like a short circuit hence all the current from the current source (4 amps) feeds R1 || R2 and produces a terminal voltage of 4 amps x 2.4 ohms = 9.6 volts.

This implies a current through R1 of 2.4 amps and a current through R2 of 1.6 amps.