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

Variation of Parameters, system of equations

  • Thread starter Linday12
  • Start date
  • #1
54
0

Homework Statement


y''+25y=cot(5x)
Find one possible solution


The Attempt at a Solution


I don't have any background in linear algebra, so I can't use cramers rule as a heads up, so I have to solve the system of equations (no linear algebra for this course is needed).

Ok, so I take the auxiliary, r^2=-25, r=+/-5i

y_h=Acos(5x)+Bsin(5x)

y_1=cos(5x) y_2=sin(5x)

Then,
u_1'cos(5x)+u_2'sin(5x) = 0
-5u_1'sin(5x)+5u_2'cos(5x) = cot(5x)

I am stumped at how to solve this system of equations. I think the rest before it is right..?

Seems like the algebra has got me.
 

Answers and Replies

  • #2
54
0
Perhaps I'm going about this completely wrong then. How would I start out solving y''+25y=cot(5x).

(I should be more specfic, when I say solve, I mean to find A solution, so y_h and y_p. I'm just not sure about how to find the y_p=u1(y_1)+u2(y_2))
 
  • #3
rock.freak667
Homework Helper
6,230
31
Ok, so I take the auxiliary, r^2=-25, r=+/-5i

y_h=Acos(5x)+Bsin(5x)

y_1=cos(5x) y_2=sin(5x)

Then,
u_1'cos(5x)+u_2'sin(5x) = 0
-5u_1'sin(5x)+5u_2'cos(5x) = cot(5x)

I am stumped at how to solve this system of equations. I think the rest before it is right..?

Seems like the algebra has got me.
u1' = -u2'tan(5x), sub that into the other equation.

this may help you as well sin2x+cos2x=1

Though, you could just use the direct result to make this easier. You are sure you can't use the Wronskian?
 

Related Threads on Variation of Parameters, system of equations

Replies
2
Views
2K
Replies
1
Views
3K
Replies
1
Views
2K
Replies
1
Views
1K
Replies
1
Views
1K
Replies
2
Views
3K
Replies
2
Views
3K
Replies
1
Views
1K
Replies
1
Views
2K
Replies
1
Views
1K
Top