CUET · MATHS · PYQ PAPER 2023
The differential equation of the family of parabolas \(y^2=4 a x\) where \(a\) is an arbitrary constant is :
- A \(2 x \frac{d y}{d x}=y\)
- B \(x \frac{d y}{d x}=y\)
- C \(y \frac{d y}{d x}=\frac{x}{2}\)
- D \(2 y \frac{d y}{d x}=x^2\)
Answer & Solution
Correct Answer
(A) \(2 x \frac{d y}{d x}=y\)
Step-by-step Solution
Detailed explanation
\(y^2 = 4ax\) \(2y \frac{dy}{dx} = 4a\) \(a = \frac{y}{2} \frac{dy}{dx}\) \(y^2 = 4 \left( \frac{y}{2} \frac{dy}{dx} \right) x\) \(y^2 = 2yx \frac{dy}{dx}\) \(y = 2x \frac{dy}{dx}\) \(2x \frac{dy}{dx} = y\)
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