Y'' + py'+ qy = 0 explain why the value of y''(a) is determined by the values of y(a)

  • Thread starter AndreaA
  • Start date
2
0
Indicate why we can impose only n initial conditions on a solution of nth order linear differential equation.

A) Given the equation y'' + py'+ qy = 0
explain why the value of y''(a) is determined by the values of y(a) and y'(a).

B) Prove that the equation y'' - 2y' -5y =0
has the solution satisfying the conditions y(0) = 1, y'(0) = 0, and y''(0) = C
if and only if C = 5.
 
Re: Y'' + py'+ qy = 0 explain why the value of y''(a) is determined by the values of

A) Given the equation y'' + py'+ qy = 0
explain why the value of y''(a) is determined by the values of y(a) and y'(a).
The DE is linear so it must have a general solution which is a linear combination of two linearly independent solutions y1(x) and y2(x).

y(x)=c1y1(x) + c2y2(x) .

c1 and c2 can be determined uniquely from the given initial conditions. So the result can be deduce from here.
 
382
4
Re: Y'' + py'+ qy = 0 explain why the value of y''(a) is determined by the values of

Do you need to the dimension of the solution set to a second order system is two dimensional?
 

AlephZero

Science Advisor
Homework Helper
6,953
291
Re: Y'' + py'+ qy = 0 explain why the value of y''(a) is determined by the values of

A) Given the equation y'' + py'+ qy = 0
explain why the value of y''(a) is determined by the values of y(a) and y'(a).
Because y''(a) = -py'(a) - qy(a).

Move along, please, there's nothing to explain here...
 

Related Threads for: Y'' + py'+ qy = 0 explain why the value of y''(a) is determined by the values of y(a)

Replies
1
Views
2K
  • Last Post
Replies
6
Views
1K
Replies
5
Views
2K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
1
Views
2K
Replies
6
Views
3K
  • Last Post
Replies
1
Views
2K
Replies
1
Views
2K

Hot Threads

Top