CUET · MATHS · PYQ PAPER 2023
The solution of the differential equation \(\frac{d y}{d x}=-\frac{x}{y}\) is:
- A \(x^2+y^2=2 C\), where \(C\) is constant of integration.
- B \(x-y^2=2 C\), where \(C\) is constant of integration.
- C \(x^2+y=2 C\), where \(C\) is constant of integration.
- D \(x^2-y^2=2 C\), where \(C\) is constant of integration.
Answer & Solution
Correct Answer
(A) \(x^2+y^2=2 C\), where \(C\) is constant of integration.
Step-by-step Solution
Detailed explanation
\(y \, dy = -x \, dx\) \(\int y \, dy = \int -x \, dx\) \(\frac{y^2}{2} = -\frac{x^2}{2} + C'\) \(x^2 + y^2 = 2C'\) \(x^2 + y^2 = 2C\)
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