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Math 303: Midterm 2 Answers November 14, 2007
 

Summary: Math 303: Midterm 2 Answers
November 14, 2007
1. The functions y1 = e2x
and y2 = e3x
are solutions to the differential equation
y - 5y + 6y = 0.
a. (10 points) Verify that y1 and y2 are linearly independent.
W(y1, y2) =
e2x
e3x
2e2x
3e3x = e5x
= 0
b. (10 points) Find a solution satisfying the initial conditions y(0) = 1 and y (0) = 4.
y = c1y1 + c2y2 = c1e2x
+ c2e3x
y(0) = c1 + c2 = 1
y (0) = 2c1 + 3c2 = 4
c1 = -1, c2 = 2, y = -e2x
+ 2e3x

  

Source: Anderson, Michael - Department of Mathematics, SUNY at Stony Brook

 

Collections: Mathematics