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The input capacitor should be fine. The output capacitor may be alright, but I can't guarantee it. If the 10uF capacitor is an electrolytic and has ESR on the order of 100mOhm up to 1Ohm, then it should be fine.
There are two potential solutions to any instability at the output of the regulator:
1. A larger output capacitor.
2. A 1 Ohm ESR in series with the 10uF capacitor. If you cannot increase the 10uF capacitor, a 1 Ohm resistor in series with the capacitor would be good to help stabilize the output.
