Finding general solution of differential equation.

Question

How general solution of this form of differential equation can be found? $$\frac {dy}{dx} = \frac {2y}{x}$$

Dennis Gulko · Accepted Answer · 2012-11-23 17:07:13Z

up vote 1 down vote accepted

$$\frac{dy}{dx}=\frac{2y}{x} \hspace{10pt}\Leftrightarrow \hspace{10pt}\frac{dy}{2y}=\frac{dx}{x}$$ Now you just need to integrate.

answered Nov 23 '12 at 17:07

Dennis Gulko
10.1k1233

1

@TPStar: It is a separable ODE. – Babak S. Nov 23 '12 at 17:08

Indeed, that's what I wrote... – Dennis Gulko Nov 23 '12 at 17:18

okay that becomes $$\frac {y^2}{4}dy = \log xdx$$ am i right? – TPSstar Nov 23 '12 at 17:28

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No, That becomes $\frac12\ln y=\ln x+C$ and so $y=Cx^2$ – Dennis Gulko Nov 23 '12 at 17:32

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