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The General Solution of the Differential Equation Y D X − X D Y Y = 0 , is

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Question

The general solution of the differential equation \[\frac{y dx - x dy}{y} = 0\], is

Options

  • xy = C

  • x = Cy2

  • y = Cx

  • y = Cx2

MCQ
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Solution

y = Cx

 

We have,

\[\frac{y dx - x dy}{y} = 0\]

\[ \Rightarrow y dx = x dy\]

\[ \Rightarrow \frac{1}{y}dy = \frac{1}{x}dx\]

Integrating both sides, we get

\[\int\frac{1}{y}dy = \int\frac{1}{x}dx\]

\[ \Rightarrow \log y = \log x + D\]

\[ \Rightarrow \log y - \log x = \log C\]

\[ \Rightarrow \log\left( \frac{y}{x} \right) = \log C\]

\[ \Rightarrow \frac{y}{x} = C\]

\[ \Rightarrow y = Cx\]

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Chapter 21: Differential Equations - MCQ [Page 144]

APPEARS IN

R.D. Sharma Mathematics Volume 1 and 2 [English] Class 12
Chapter 21 Differential Equations
MCQ | Q 52 | Page 144

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