A differential equation may have multiple solutions. The reverse is also true: a function can be a solution of many differential equations. One example suffices to illustrate this.

Consider the function \[y(t)=\frac{1}{t}\tiny.\] You know that \[y'(t)=-\frac{1}{t^2}\tiny.\] But on the right-hand side of this formula, you may also write \[y'(t)=-\frac{y(t)}{t}\] or \[y'(t)=-y(t)^2\] or \[y''(t)=-2y(t)y'(t)\] and still have a differential equation of which the given function is a solution.