can someone help me with reduced the partial differential equation
du/dt = - f(x) d^2 u/ dx^2 - g(x) du/dx --- (1)
to become:
du/dt = - p(x) d^2 u/ dx^2 --- (2)
then eqn. (2) is solved by using the separation of variables methods or Fourier transformation.
eqn. (1) is linear second order homogeneous partial differential equation with variable coefficients. This kind of equations is called usually the heat-Like equation where f(x), g(x) and p(x) are variables coefficients.
also, is there another method to solve this kind of equations? if the answer is yes, then what is the method and how it apply to eqn. (1)
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