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Home  >>  CBSE XII  >>  Math  >>  Differential Equations

The integrating factor of the differential equation $x\large\frac{dy}{dx}$$-y=2x^2 $ is

\[(A)\;e^{-x}\qquad(B)\;e^{-y}\qquad(C)\;\frac{1}{x}\qquad(D)\;x\]

1 Answer

Toolbox:
  • If the equation is of the form $\large\frac{dy}{dx}$$ + py= Q$, then the integrating factor is $e^{\large\int pdx}$
The equation can be rewritten as $\large\frac{dy}{dx }-\frac{ y}{x} =$$ 2x^2$
Here $p = \large\frac{-1}{x}$ and $Q = 2x^2$
Hence the integral Factor is $e^{\int (\large\frac{-1}{x})}dx = e^{\large-\log x} = e^{\large \log(1/x)} = 1/x$
Hence C is the correct answer.
answered Jul 30, 2013 by sreemathi.v
 
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