Summary of Particular Solution Methods

We have illustrated three possible methods to find particular solutions. Each has certain advantages and disadvantages, which are summarized as follows. 

This technique has advantages for elementary polynomial forcing functions (e.g., 2x + 1, 5jc + 3, etc.), and it is easy to apply and use. However, it becomes quite tedious to use on trigonometric forcing functions, and it is not faQ-safe in the sense that some experience is necessary in constructing the trial function. Also, it does not apply to equations with nonconstant coefficients. 

This method is the quickest and safest to use with exponential or trigonometric forcing functions. Its main disadvantage is the necessary amount of new material a student must learn to apply it effectively. Although it can be used on elementary polynomial forcing functions (by expanding the inverse operators into ascending polynomial form), it is quite tedious to apply for such conditions. Also, it cannot be used on equations with nonconstant coefficients. 

This procedure is the most general method, since it can be applied to equations with variable coefficients. Although it is fail-safe, it often leads to intractable integrals to find F. and It is the method of choice when treating forced problems in transport phenomena, since both cylindrical and spherical coordinate systems always lead to equations with variable coefficients. 

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