Typical Forms of The Particular Integral
In order to find the particular integral, we need to 'guess' its form, with some coefficients left as variables to be solved for. This takes the form of the first derivative of complementary function. Below is a table of some typical functions and the solution to guess for them.
| Function of x | Form for y |
If a term in the above particular integral for y appears in the homogeneous solution, it is necessary to multiply by a sufficiently large power of x in order to make the independent]]. If the function of x is a sum of terms in the above table, the particular integral can be guessed using a sum of the corresponding terms for y.
Read more about this topic: Method Of Undetermined Coefficients
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