This is just something I've asked myself, and not something I need help with for school.
Does the differential equation have any nontrivial solutions?
If it is not requested that is valid for every t but for 'almost every t' we have several 'candidate functions'. One of the most simple is the periodic function with period T=1 defined as...
Very suggestive is also the 'PSK modulated' periodic function with period T=4 defined as...