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.