Chapter 13.1, Problem 17E

To determine

To show:

The solutions to the problems

$y^{\prime }\left(x\right)=f\left(x,y\left(x\right)\right)$, $y\left(x_0\right)=y_0$

and

$y\left(x\right)=y_0+{\displaystyle \underset{x_0}{\overset{x}{\int }}f\left(t,y\left(t\right)\right)dt}$

are same.