Finding Solutions to IVPs with Continuous Coefficients

  • Thread starter Thread starter stanford1463
  • Start date Start date
  • Tags Tags
    General Ivp
stanford1463
Messages
44
Reaction score
0

Homework Statement


Find all solutions of the IVP y'' + a(t)y' + b(t)y = 0, y(t0) = 0, y'(t0) = 0 where t0 is any fixed point on the t-axis and the coefficients are continuous.


The Attempt at a Solution


I know this has to do with the Existence and Uniqueness theorem. How would I apply that and solve this? Is the general solution y = c1y1 + c2y2? I'm not sure how to solve this...
 
Physics news on Phys.org
Bump...any suggestions?
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
View full post »

Similar threads

Avoid unpleasant integrals in solving IVP
Replies
3
Views
2K
Existence and Uniqueness For ODE
Replies
6
Views
2K
Prove that solutions to autonomous first order DE can't have local maxima
Replies
2
Views
1K
First-order nonlinear differential equation
Replies
6
Views
2K
How to get general solution via Green's function?
Replies
1
Views
1K
ODE's: IVP Existence/Uniqueness
Replies
2
Views
2K
IVP ODE checking specifics of solution
Replies
1
Views
1K
Show uniqueness in Dirichlet problem in unit disk
Replies
6
Views
1K
Laplace Transform for Solving a First Order Linear IVP
Replies
26
Views
3K
Laplace (IVP): Having Trouble Understanding Solution Manual's Answer
Replies
7
Views
2K

Hot Threads

Recent Insights

Back
Top