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NDA 2018
Exam
NDA
Year
2018
Subject
Mathematics
Chapter
Differential Equations

NDA 2018 · Mathematics · Differential Equations

What is the solution of the differential equation x d y-y d x=0 ?

What is the solution of the differential equation xdy−ydx=0?x d y-y d x=0 ?

Options

  1. Axy=cx y=c
  2. By=cx\mathrm{y}=\mathrm{cx}
  3. Cx + y = c
  4. Dx – y = c

Correct answer

B. y=cx\mathrm{y}=\mathrm{cx}

Step-by-step solution

xdy−ydx=0⇒xdy=ydx⇒dyy=dxx⇒log⁡y=log⁡x+log⁡c⇒log⁡y−log⁡x=log⁡c⇒log⁡(yx)=log⁡c⇒yx=c⇒y=cx\begin{aligned} & x d y-y d x=0 \\ & \Rightarrow x d y=y d x \\ & \Rightarrow \frac{d y}{y}=\frac{d x}{x} \\ & \Rightarrow \log y=\log x+\log c \\ & \Rightarrow \log y-\log x=\log c \\ & \Rightarrow \log \left(\frac{y}{x}\right)=\log c \\ & \Rightarrow \frac{y}{x}=c \Rightarrow y=c x\end{aligned}
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