Answer
$$y =c_1e^{\sin x}$$
Work Step by Step
Given $$y-\frac{dy}{dx}\sec x=0 $$
Then
$$\frac{dy}{dx}=y \cos x$$
Separate variables
\begin{align*}
\int \frac{dy}{ y} &= \int \cos xdx \\
\ln y&=\sin x+c \\
y&=e^{\sin x+c}\\
&=c_1e^{\sin x}
\end{align*}