Since the left- and right- hand sides of the d.e. are the same, y = xnis a solution to this differential equation.
You may also encounter problems that look something like this:
Show that the function such-and-such is a solution to the d.e. blah-blah."
While the word "show" may strike terror in your heart, don't give in to fear! Problems that say "show" are actually easier than ones that look like this:
"Determine whether the function such-and-such is a solution to the d.e. blah-blah."
Regardless of whether a problem says "show" or "determine", do the same thing: evaluate the left-hand side of the d.e., evaluate the right-hand side of the d.e., and see if you get the same thing from both sides.
Here's the difference between these types of problems: If a problem says "determine," you need to figure out whether the function is a solution to the d.e. or not. If a problem says "show," it's telling you the answer you'll get if you do the work right.