Chapter 8 - Mathematical Modeling With Differential Equations - 8.2 Separation Of Variables - Exercises Set 8.2 - Page 575: 10

$$y =c_1e^{\sin x}$$

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*}