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Home  >>  CBSE XII  >>  Math  >>  Differential Equations
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The general solution of the differential equation $\large\frac{ydx-xdy}{y}$$=0\;is$

\[(A)\;xy=C\qquad(B)\;x=Cy^2\]\[(C)\;y=Cx\qquad(D)\;y=Cx^2\]

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  • 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.
answered Jul 29, 2013 by sreemathi.v
edited Jul 29, 2013 by sreemathi.v
 

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