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CUET · MATHS · PYQ PAPER 2025

The differential equation representing the curve \(y=e^{2 x}(a+b x)\), where \(a, b\) are arbitrary constants is

  1. A \(\frac{d^2 y}{d x^2}+4 \frac{d y}{d x}+4 y=0\)
  2. B \(\frac{d^2 y}{d x^2}-4 \frac{d y}{d x}-4 y=0\)
  3. C \(\frac{d^2 y}{d x^2}-4 \frac{d y}{d x}+4 y=0\)
  4. D \(\frac{d^2 y}{d x^2}+4 \frac{d y}{d x}-4 y=0\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{d^2 y}{d x^2}-4 \frac{d y}{d x}+4 y=0\)

Step-by-step Solution

Detailed explanation

\( \frac{dy}{dx} = 2e^{2 x}(a+b x) + be^{2 x} \) \( \frac{dy}{dx} = 2y + be^{2 x} \) \( \frac{d^2y}{dx^2} = 2 \frac{dy}{dx} + 2be^{2 x} \) \( \frac{d^2y}{dx^2} = 2 \frac{dy}{dx} + 2 \left( \frac{dy}{dx} - 2y \right) \) \( \frac{d^2y}{dx^2} = 4 \frac{dy}{dx} - 4y \)…