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AP EAMCET · Maths · Differential Equations

The general solution of \(x d y-y d x=y d y\) is

  1. A \(y=A e^{-x / y}\)
  2. B \(y=A e^x\)
  3. C \(\frac{y}{x}=A e^x\)
  4. D \(\frac{x}{y}+\frac{y}{x}=c\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(y=A e^{-x / y}\)

Step-by-step Solution

Detailed explanation

\(x d y-y d x=y d y\) \(\begin{aligned} & \Rightarrow \quad-(y d x-x d y)=y d y \\ & \Rightarrow \quad-\left(\frac{y d x-x d y}{y^2}\right)=\frac{y d y}{y^2}\end{aligned}\) \(\Rightarrow \quad-\int d\left(\frac{x}{y}\right)=\int \frac{d y}{y}\)…