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Differential equations

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Please show all steps.

section 6.4 # 2,4,6,14
section 7.2 #4,12,18,31

See attached.

Use the method of variation of parameters...
Determine the Laplace transform....
use the Laplace transform table and the linearity of the Laplace transform to determine the following transforms...

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Solution Summary

This provides examples of working with differential equations, including word problems, Laplace transforms, and variation of parameters to find a particular solution.