Hi and Welcome!
a slim DVD writer requires 1.5A@5V. An USB port is specified for 500mA@5V, so there is a 300% overload of the USB port the drive is connected to. The (spec-incompliant) Y-cable doesn't help much here.
That said, it is really a good idea to use an USB hub with power supply if there can't be a power supply attached to the drive directly.