CUET · MATHS · PYQ PAPER 2025
If \(y=\sqrt{x+\sqrt{x+\sqrt{x+\cdots}}}\), then
- A \((2 y+1) \frac{d y}{d x}+3 \sqrt{x}=0\)
- B \(3 \frac{d y}{d x}+3 y^2=0\)
- C \(3 x \frac{d y}{d x}+(2 y+1)=0\)
- D \((2 y-1) \frac{d y}{d x}-1=0\)
Answer & Solution
Correct Answer
(D) \((2 y-1) \frac{d y}{d x}-1=0\)
Step-by-step Solution
Detailed explanation
\(y=\sqrt{x+y}\) \(y^2=x+y\) \(2y \frac{dy}{dx} = 1+\frac{dy}{dx}\) \((2y-1)\frac{dy}{dx}=1\) \((2y-1)\frac{dy}{dx}-1=0\)
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