Description of The Method
Consider a linear non-homogeneous ordinary differential equation of the form
The method consists of finding the general homogeneous solution for the complementary linear homogeneous differential equation
and a particular integral of the linear non-homogeneous ordinary differential equation based on . Then the general solution to the linear non-homogeneous ordinary differential equation would be
If consists of the sum of two functions and we say that is the solution based on and the solution based on . Then, using a superposition principle, we can say that the particular integral is
Read more about this topic: Method Of Undetermined Coefficients
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—Horace Walpole (1717–1797)
“The next Augustan age will dawn on the other side of the Atlantic. There will, perhaps, be a Thucydides at Boston, a Xenophon at New York, and, in time, a Virgil at Mexico, and a Newton at Peru. At last, some curious traveller from Lima will visit England and give a description of the ruins of St Paul’s, like the editions of Balbec and Palmyra.”
—Horace Walpole (1717–1797)
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—Ralph Waldo Emerson (1803–1882)