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Differential equations - variation of parameters

  • #1

Homework Statement


Find a particular solution using variation of parameters.
y'' + 3y' + 2y = 4e^x

Homework Equations


yp = -y1 * INT (y2f(x)/W[y1,y2]) dx + y2 * INT (y1f(x)/W[y1,y2]) dx

The Attempt at a Solution


So, first I find the homogeneous solution, correct?
r2 + 3r + 2 = 0, so the roots are - 1 and -2, so
yh = c1 * e-x + c2 * e-2x
Then, I use the variation of parameters formula:
yp1 = -y1 * INT (y2f(x)/W[y1,y2]) dx
= 2/3ex

yp1 = y2 * INT (y1f(x)/W[y1,y2]) dx
= -4ex

Adding them together, yp = yp1 + yp2 = -10/3ex.

However, the answer is just 2/3ex, what I got for yp1.
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
25,832
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hi mbradar2! :smile:

i think you added instead of subtracting in your determinant for W :wink:
 

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