For the differential equation, find (a) one solution and then (b) all solutions.
y' = x5
When we take the derivative of a polynomial the degree drops by 1, so this almost looks like it came from taking the derivative of the function y = x6. However, the derivative of x6 is 6x5. To cancel out the extra 6 we get when taking the derivative, we need to introduce a factor of . A solution tothe differential equation could look like this:
All solutions look like this (for any constant C):