The solution of the differential equation \(\displaystyle\frac{dy}{dx}=-\frac{x}{y}\) is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(x^2+y^2=2C\), where C is constant of integration.
The equation is in variables separable form:
\(y\,dy = -x\,dx\)
Integrating both sides:
\( \displaystyle \frac{y^2}{2} = -\frac{x^2}{2} + C \)
Multiplying by 2:
\(y^2 = -x^2 + 2C\)
\(x^2 + y^2 = 2C\)