Answer to Question #247049 in Differential Equations for Sarah

Question

(2+ycosx)dx+cosxdy=0

Answer 1

$$y'+y=-\dfrac{2}{\cos x}$$

Integrating factor

$$\mu(x)=e^x$$

$$e^xy'+e^xy=-\dfrac{2e^x}{\cos x}$$

$$d(e^xy)=-\dfrac{2e^x}{\cos x}dx$$

Integrate

$$\int d(e^xy)=-\int \dfrac{2e^x}{\cos x}dx$$

$$e^xy=-\int \dfrac{2e^x}{\cos x}dx$$

$$y=-e^{-x}\int \dfrac{2e^x}{\cos x}dx$$