- #1

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- 143

\frac{{dy}}{{dx}} = \frac{{4x^2 + 5xy + y^2 }}{{x^2 }} \\

\\

\frac{{dy}}{{dx}} = 4 + \frac{{5y}}{x} + \left( {\frac{y}{x}} \right)^2 \\

\\

{\rm{Let }}v = y/x\,\,\,\, \Rightarrow \,\,\,\,y = vx \\

\\

\frac{{dy}}{{dx}} = 4 + \frac{{5v}}{{xx}} + \left( {\frac{{vx}}{x}} \right)^2 \\

\\

\frac{{dy}}{{dx}} = 4 + \frac{{5v}}{{x^2 }} + v^2 \\

\end{array}[/tex]

But the class notes say the final line should be

[tex]\frac{dy}{dx}=x\frac{dv}{dx}+v[/tex]

How did he get that?