Topic: Engineering Mathematics
The solution of ODE $y~dx+x~dy=0$ is
- A. $y=\frac{k}{x}$
- B. $y=\frac{k}{y-x}$
- C. $y=\frac{x}{y}$
- D. $y=e^{kx}$
Answer: A. $y=\frac{k}{x}$
Explanation: Separating the variables: $\frac{dx}{x} = -\frac{dy}{y}$. Integrating both sides: $\ln x = -\ln y + \ln k \Rightarrow \ln x + \ln y = \ln k \Rightarrow \ln(xy) = \ln k \Rightarrow xy = k \Rightarrow y = \frac{k}{x}$.