CUET · MATHS · PYQ PAPER 2025
If \(y=3 e^{2 x}+2 e^{3 x}\), then \(\frac{d^2 y}{d x^2}+6 y\) is equal to:
- A \(\frac{d y}{d x}\)
- B \(5 \frac{d y}{d x}\)
- C \(6 \frac{d y}{d x}\)
- D \(30 \frac{d y}{d x}\)
Answer & Solution
Correct Answer
(B) \(5 \frac{d y}{d x}\)
Step-by-step Solution
Detailed explanation
\(y = 3e^{2x} + 2e^{2x} = 5e^{2x}\) \(\frac{dy}{dx} = \frac{d}{dx}(5e^{2x}) = 10e^{2x}\) \(\frac{d^2y}{dx^2} = \frac{d}{dx}(10e^{2x}) = 20e^{2x}\) \(\frac{d^2 y}{d x^2}+6 y = 20e^{2x} + 6(5e^{2x}) = 20e^{2x} + 30e^{2x} = 50e^{2x}\) \(50e^{2x} = 5(10e^{2x}) = 5 \frac{dy}{dx}\)
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