# Variation of parameters and Undetermined coeeficients

1. Write a short paragraph comparing and contrasting the method of undetermined coefficients and variation of parameters. How are they similar, how they are different? If you had your choice, which method would you use?

2. Consider the differential equation:

my"+cy'+ky=mg+sqrt(t)

Why would the method of undetermined coefficients be difficult to use for this problem?

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#### Solution Preview

Hi there!

Here is the short description of the two methods.

Note that in the second problem Q(x)exp(a*x)cos(beta*x) should read Q(x)exp(a*x)sin(beta*x)

You might want to check for more complete overview (the assignmant called for only few paragraphs) the site:

http://sosmath.com/diffeq/diffeq.html

esp.

http://sosmath.com/diffeq/second/guessing/guessing.html

http://sosmath.com/diffeq/second/variation/variation.html

Please use complete sentences. Avoid using abbreviations. Use a math symbol editor like Latex. Please, no stuff like <=.

1. The method of undetermined coefficients (MUC) is a very elegant method to find a particular solution for a non-homogenous ODE with constant coefficients: . Once the solution to the associated homogenous equation is found, ...

#### Solution Summary

The solution discusses the advantages and disadvantages of each method.