The LM337K can handle a maximum input voltage of 40V, but it's recommended to keep it below 35V for reliable operation.
To ensure stability, use a minimum output capacitance of 10uF, and keep the output voltage sense lines short and away from the input voltage lines. Also, use a low-ESR capacitor for the output filter.
The LM337K requires a minimum load current of 3.5mA to regulate properly. If the load current is less than this, the output voltage may not be regulated accurately.
The LM337K is rated for operation up to 125°C, but its performance may degrade at high temperatures. It's recommended to derate the output current and voltage at high temperatures to ensure reliable operation.
Use a TVS (Transient Voltage Suppressor) diode or a voltage clamp circuit at the input to protect the LM337K from voltage transients and spikes.