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NDA2021MathematicsDifferential EquationsActual

Which one of the following differential equations has the general solution y=a e^x+b e^ -x ?

Options

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

Correct answer

B. d^2 y d x^2 -y=0

Step-by-step solution

aligned & y=a e^x+b e^ -x & d y d x =a e^x-b e^ -x aligned aligned & d^2 y d x^2 =a e^x+b e^ -x d^2 y d x^2 =y & d^2 y d x^2 -y=0 aligned

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