What is the differential equation of the family of straight lines passing through the origin?
\(x\dfrac{dy}{dx}-y=0\)
Every line through the origin can be written as \(y=mx\), so \(\dfrac{dy}{dx}=m=\dfrac{y}{x}\). Eliminating the constant \(m\) gives \(x\dfrac{dy}{dx}-y=0\).
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