Chapter 2 - First Order Differential Equations - 2.2 Separable Equations - Problems - Page 47: 3

$y=\frac{1}{c-\cos x}$

$\frac{dy}{dx}+y^2\sin(x)=0$ Separate variables: $\frac{dy}{dx}=-y^2\sin(x)$ $\frac{dy}{y^2}=-\sin(x)dx$ Integrate: $-\int{\sin(x)dx}=\int{y^{-2}dy}$ $\cos(x)=-\frac{1}{y}+c$ $\frac{1}{y}=c-\cos x$ $y=\frac{1}{c-\cos x}$