satisfy (someone or an animal) with something
to use something to please or content someone or an animal. Do you think I can satisfy Mrs. Franklin with payment for her broken window? A dog biscuit will satisfy the dog until its regular feeding time.
satisfy something by something
and satisfy something with somethingto fulfill a requirement, using a particular thing, such as a school or college course. Can I satisfy the requirements by taking a course in art? Will I satisfy the requirement with this course?