Chapter 5 - The Integral - 5.3 The Indefinite Integral - Exercises - Page 253: 57

$y=\frac{1}{5}sin(5x)+3$

$\frac{dy}{dx}=cos(5x);$ $y(\pi)=3$ $dy=cos(5x)dx$ $\int dy=\frac{1}{5}\int5cos(5x)dx$ $y=\frac{1}{5}sin(5x)+C$ Substitute in the initial condition to solve for $C$ $3=\frac{1}{5}sin(5\pi)+C$ $C=3$ $y=\frac{1}{5}sin(5x)+3$