 
Summary: Mathematics 3C
Worksheet 7, Firstorder linear DE's
Fall 2011, Kennedy
NAME:
Website: http://math.ucsb.edu/kgracekennedy/Fall2011 3C.html
Course Website: Access through GauchoSpace.
Variation of Parameters
Use clear presentation and justify every step.
1. What kinds of DE can be solved using variation of parameters?
2. What are the three steps of solving these DE's using variation of param
eters?
3. Solve the following DE using variation of parameters:
y (t) + y(t) = t
(a) Find the homogeneous solution yh.
(b) Find a particular solution yp.
(c) What is the general solution?
Why is the last step valid? 1
1Hint: Substitute the sum into the left side and use the fact yh is the solution to the
homogeneous DE.
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