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Separation of variables method is also termed as

  • A.Laplace method
  • B.Fourier method
  • C.Len method
  • D.Gauss method

Answer: B

Separation of variables is also called the Fourier method, after Fourier's use of it on the heat equation.

The idea is to look for a solution built as a product of single-variable functions:

\[ u(x,t) \;=\; X(x)\,T(t) \]

Substituting and dividing through leaves each side depending on one variable only, so both must equal a constant. That turns one partial differential equation into two ordinary ones, whose solutions are then recombined as a Fourier series.

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