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The differential equation of the form 1 - x²)y^′′ - 2xy' + n(n + 1)y 0 is called?
  1. Legendre equation
  2. Hermite equation
  3. Cauchy equation
  4. None of these
Explanation

The differential equation (1 - x²)y'' - 2xy' + n(n + 1)y = 0 is known as Legendre's equation.

It arises in problems with spherical symmetry, such as solutions to Laplace’s equation in spherical coordinates.

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If y = 2x and z = 5y, then x + 3y + z = ?
  1. 15x
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