• Support PF! Buy your school textbooks, materials and every day products Here!

What did I do Wrong?

  • #1
1,010
1
What did I do Wrong??

Homework Statement



Find a particular solution yp of the differential equation
[tex] 9y''+5y'+2y=sin^2(x) [/tex]

using the Method of Undetermined Coefficients. Primes denote derivatives with respect to x.

Homework Equations



[tex] sin^2(x) = \frac{1-cos(2x)}{2} [/tex]

The Attempt at a Solution



Possible derivatives
  • A
  • B cos(2x)
  • C sin(2x)

[tex] y_p = A + Bcos(2x) + Csin(2x) [/tex]

[tex] y_p' = -2Bsin(2x) + 2Ccos(2x) [/tex]

[tex] y_p'' = -4Bcos(2x) + -4Csin(2x) [/tex]

Sub back into original modified with cos substitution on the right

[tex] 9y''+5y'+2y = \frac{1-cos(2x)}{2} [/tex]

Becomes

[tex] 9[-4Bcos(2x) + -4Csin(2x)] + 5[-2Bsin(2x) + 2Ccos(2x)] + 2[A + Bcos(2x) + Csin(2x)] = \frac{1-cos(2x)}{2} [/tex]

From that I get
2A = 1/2 => A=1/4

-36B + 10C + 2B = -1/2
-36C + -10B + 2C = 0

Solving for B and C
Leads to

[tex]y_p = (1/4)+(17/1056)*cos(2*x)+(5/1056)*sin(2*x) [/tex]

Where
B = 17/1056
and
C = 5/1056
 
Last edited:

Answers and Replies

  • #2
arildno
Science Advisor
Homework Helper
Gold Member
Dearly Missed
9,970
131
Spare us the decimals. Please!!
 
  • #3
150
0
Did you check your answer by plugging it into the diff. eq.? (I'm sure you will see that A is wrong at least.)
 
  • #4
1,010
1
I realized I type it wrong when i had A defined, but i had it correct or so I thought in the equation A=1/4
 
  • #5
AKG
Science Advisor
Homework Helper
2,565
4
-36B + 10C + 2B = -1/2
-36C + -10B + 2C = 0

Where
B = 17/1056
and
C = 5/1056
You solved for A correctly, but B and C are wrong.
 
  • #6
1,010
1
-36B + 10C + 2B = -1/2
-36C + -10B + 2C = 0

-34B + 10 C = -1/2
-10B + -34C = 0

34B + 115.6C = 0
125.6C=-1/2

C = -5/1256

Therefore B equal

-10B + -34C = 0

B = 17/1256


I am down to one final attempt at this problem can someone confirm this correct?


[tex]y_p = (1/4)+(17/1256)*cos(2*x)+(-5/1256)*sin(2*x) [/tex]
 
  • #7
Dick
Science Advisor
Homework Helper
26,258
618
That's what I get.
 
  • #8
1,010
1
Algerbra FTW

... eh wow I feel stupid

it worked!
 

Related Threads on What did I do Wrong?

  • Last Post
Replies
1
Views
2K
Replies
2
Views
814
  • Last Post
Replies
5
Views
2K
Replies
9
Views
2K
Replies
2
Views
1K
Replies
1
Views
855
Replies
1
Views
2K
Replies
13
Views
2K
Replies
7
Views
6K
Replies
4
Views
941
Top