So far we have changed only the dependent variable. It is also possible to change the in...

So far we have changed only the dependent variable. It is also possible to change the independent variable to obtain a new equation. This is analogous to changing the way we measure time. Consider the differential equation

This differential equation could be solved using an integrating factor, but we will use a change of variables. Suppose we define a new time variable (a new independent variable) using the formula

(a) Show that dy/ds = y + s.

(b) Find the general solution of the differential equation with the variable s.

(c) What is the general solution of the original differential equation?