Question

Which separable equation follows from \[x\frac{dv}{dx}=\frac{1}{\cos v}\]?

Options

• \[dv=\cos v\,dx\]

• \[\frac{dv}{\cos v}=\frac{dx}{x}\]

• \[\cos v\,dv=\frac{dx}{x}\]

• \[\cos v\,dv=x\,dx\]

Answer 1

Multiply by \[\cos v\,dx\] and divide by \[x\]. This separates the variables as \[\cos v\,dv=\frac{dx}{x}\].