Diff Eq- Nonhomogeneous Equations

  • Thread starter Totalderiv
  • Start date
  • #1
70
1

Homework Statement


Find a particular solution of the given equation.
[tex] y^''' + 4y^' = 3x-1[/tex]

Homework Equations



[tex] r^3 + 4r = 0 [/tex]
[tex] r = 0, r = 2i, r = -2i[/tex]

The Attempt at a Solution


[tex]y(x) = Ax-B[/tex]
[tex]y^'(x) = A[/tex]
[tex]y^''(x) = 0[/tex]
[tex]y^'''(x) = 0[/tex]


The answer is:
[tex]y(x)=(3/8)x^2 - (1/4)x[/tex]
But I'm not sure how they came to this, please help!!!
 

Answers and Replies

  • #2
LCKurtz
Science Advisor
Homework Helper
Insights Author
Gold Member
9,559
773
r=0 gives a constant as a solution of the homogeneous equation. So instead of trying Ax+B you must multiply by x and try ##y_p=Ax^2+Bx##.
 
  • #3
LCKurtz
Science Advisor
Homework Helper
Insights Author
Gold Member
9,559
773
Thanks! I have another question though,

[tex] 4y^'' + 4y^' + y = 3xe^x [/tex]

How do I start this?

The same way you started the other one. You find the complementary solution and then use Undetermined Coefficients for the particular solution. Surely your text discusses the method of Undetermined Coefficients, doesn't it?
 

Related Threads on Diff Eq- Nonhomogeneous Equations

Replies
1
Views
1K
Replies
4
Views
2K
Replies
1
Views
1K
Replies
3
Views
1K
Replies
2
Views
1K
  • Last Post
Replies
4
Views
7K
Replies
2
Views
5K
Replies
5
Views
785
Replies
1
Views
4K
Top