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MHT CET202522 Apr 2025Evening ShiftMathematicsDifferential EquationsActual

The differential equation satisfied by y=X (6 t+5)+Y (6 t+5) is (where X and Y are constants)

Options

  1. Ad ^2 y dt ^2 +6 y =0
  2. Bd ^2 y dt ^2 =0
  3. Cd ^2 y dt ^2 +36 y =0
  4. Dd^2 y d t^2 +25 y=0

Correct answer

C. d ^2 y dt ^2 +36 y =0

Step-by-step solution

Given the function y = X (6t + 5) + Y (6t + 5) Differentiate twice to find a relation with the original function. Differentiating y yields the first derivative: dy dt = 6X (6t + 5) - 6Y (6t + 5) A second differentiation gives: d^2y dt^2 = -36X (6t + 5) - 36Y (6t + 5) This simplifies to: d^2y dt^2 = -36 (X (6t + 5) + Y (6t + 5) ) Recognizing the original definition of y , we substitute to obtain: d^2y dt^2 = -36y Rearranged, this gives the homogeneous second-order linear differential equation: d^2y dt^2 + 36y = 0 Th

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