Question

After putting \[y=vx\] in \[\frac{dy}{dx}=\frac{y\cos\left(\frac{y}{x}\right)+x}{x\cos\left(\frac{y}{x}\right)}\], which equation results?

Options

• \[v+x\frac{dv}{dx}=\frac{v+\cos v}{\cos v}\]

• \[v+x\frac{dv}{dx}=v\cos v+1\]

• \[v+x\frac{dv}{dx}=\frac{\cos v}{v\cos v+1}\]

• \[v+x\frac{dv}{dx}=\frac{v\cos v+1}{\cos v}\]

Answer 1

Using \[y=vx\] gives \[\frac{y}{x}=v\] and \[\frac{dy}{dx}=v+x\frac{dv}{dx}\]. Cancelling \[x\] in the right-hand side gives \[\frac{v\cos v+1}{\cos v}\].