The waveform shows current leading voltage thus inductive current
L=100uH , dI = 13 A , dt = ~ 0.1 ms to 1st current peak when V~38V
V=LdI/dt = 100e-6 * 13A / 0.1ms = 13V which is the difference between 24Vdc in and 38Vdc approx.
This accounts for the rise time approx. to the step input Voltage, but not the pulse PWM which is a shorter cycle.
more clarification.
The initial Step on for 24V has a series RLC response with high Q since ESR is near 0 (DCR (L)=0.1, Rs(D1)<=0.1 Ohm
The resonant frequency is near 2kHz where L=100uH has an impedance < 1 Ohm thus giving a Q of ~ 5. This is appropriate for the observed resonant decay time.
The high surge current thus promotes the desire for a soft start circuit with slightly more turn-on time. This would be implemented with an additional series PWM controlled switch which becomes the classic Buck/Boost circuit.
However the Switcher at 100kHz makes the ZL(100uH)=50 Ohms in series with the 20 Ohm load shunted by 39uF which Zc < 0.1 Ohm (33uF @ 100kHz). Thus the impedance ratio would appear to be well damped.