Can the Fourier Transform be used to solve any Differential Equation?

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Does it have any limitations, or can it be used to solve any and all of them?

i.e. Can it solve a PDE with inhomogeneous or homogeneous boundary conditions, periodic boundary conditions, dirichlet boundary conditions, etc? Can it solve PDEs regardless of order or type (diffusion, Poisson 2-3D, Wave 1-3D, etc.)?

I ask because I am having some issues trying to use it to solve a PDE and am starting to grow suspicious of whether or not it is even applicable to my problem and whether or not I should switch methods.