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AP EAMCET20224 Jul 2022Morning ShiftMathematicsDifferential EquationsActual

y = A e x + B e - 2 x satisfies which of the following differential equations?

Options

  1. Ad 2 y d x 2 - d y d x + 2 y = 0
  2. Bd 2 y d x 2 - 2 d y d x - y = 0
  3. Cd 2 y d x - 2 d y d x + y = 0
  4. Dd 2 y d x 2 + d y d x - 2 y = 0

Correct answer

D. d 2 y d x 2 + d y d x - 2 y = 0

Step-by-step solution

y = A e x + B e - 2 x On differentiating, we get d y d x = A e x - 2 B e - 2 x Subtracting both the above equations, we get y - d y d x = 3 B e - 2 x or y e 2 x - d y d x e 2 x = 3 B Differentiating above equation, we get 2 y e 2 x + e 2 x d y d x - 2 e 2 x d y d x - e 2 x d 2 y d x 2 = 0 ⇒ 2 y - d y d x - d 2 y d x 2 = 0

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