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# The general solution of the differential equation $\large\frac{ydx-xdy}{y}$$=0\;is $(A)\;xy=C\qquad(B)\;x=Cy^2$$(C)\;y=Cx\qquad(D)\;y=Cx^2$ Can you answer this question? ## 1 Answer 0 votes Toolbox: • The linear differential equation of the form dy/dx = F(x,y), where F(x,y) is of the form g(x).h(y), where g(x) is a function of x and h(y) is a function of y is called variable seperable. Such equations can be solved by seperating the variables and integrating them. Step 1: Given \large\frac{ydx - xdy}{y}$$= 0$
$ydx=xdy$
Separating the variables we get,
(i.e)$\large\frac{dy}{y}=\frac{dx}{x}$
Step 2:
Integrating on both sides we get,
$\log y = \log x + \log C$
$\log y - \log x =\log C$
$\log\mid\large\frac{y}{x}\mid $$= \log C \large\frac{y}{x}=$$C$
Or $y=Cx$
Hence the correct option is C.
edited Jul 29, 2013