Question

Writing \[x\cos\left(\frac{y}{x}\right)\frac{dy}{dx}=y\cos\left(\frac{y}{x}\right)+x\] in standard form gives which expression?

Options

• \[\frac{dy}{dx}=y\cos\left(\frac{y}{x}\right)+x\cos\left(\frac{y}{x}\right)\]

• \[\frac{dy}{dx}=\frac{x\cos\left(\frac{y}{x}\right)}{y\cos\left(\frac{y}{x}\right)+x}\]

• \[\frac{dy}{dx}=\frac{y\cos\left(\frac{y}{x}\right)+x}{x\cos\left(\frac{y}{x}\right)}\]

• \[\frac{dy}{dx}=\frac{y+x}{\cos\left(\frac{y}{x}\right)}\]

Answer 1

Divide both sides by \[x\cos\left(\frac{y}{x}\right)\]. This gives \[\frac{dy}{dx}=\frac{y\cos\left(\frac{y}{x}\right)+x}{x\cos\left(\frac{y}{x}\right)}\], which is of the form \[\frac{dy}{dx}=F(x,y)\].