Can anyone help me to find a solution to for the attached partial differential equation ?
I want to find a general solution to a partial differential equation by assuming that I know one solution, called , and trying to find another solution by assuming that the general solution in the form of . I want to restrict the second solution to be in the form of so that it satisfies the PDE, and is a function of times . The latter makes error as the maple identifies that the function depends on only one variable . Could you please help me to find a solution for in the form ?
Also, I have trouble with defining the operator Do in the attached file. When it operates on , maple gives D. It is not clear for me that whether this derivative is with respect to or . I need is to define Do in a way so that the derivatives are correctly taken with respect to different separate variables.
Thank you for your help,