CUET · MATHS · PYQ PAPER 2023
If \(y=A \sin x+B \cos x\), then which of the following is correct?
- A \(\frac{d^2 y}{d x^2}-y=0\)
- B \(\frac{d^2 y}{d x^2}+y=0\)
- C \(\frac{d^2 y}{d x^2}=\frac{d y}{d x}\)
- D \(\frac{d^2 y}{d x^2}=-\frac{d y}{d x}\)
Answer & Solution
Correct Answer
(B) \(\frac{d^2 y}{d x^2}+y=0\)
Step-by-step Solution
Detailed explanation
\(\frac{d y}{d x}=A \cos x-B \sin x\) \(\frac{d^2 y}{d x^2}=-A \sin x-B \cos x\) \(\frac{d^2 y}{d x^2}=-(A \sin x+B \cos x)=-y\) \(\frac{d^2 y}{d x^2}+y=0\)
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