let with suppose that dependent then there exist

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: m is equivalent to the equations Finally, upon setting , The corresponding eigenvector is Hence the general solution is x Invoking the initial conditions, It follows that , and . Hence the solution of the IVP is x 19. Set x . Substitution into the system of differential equations results in A which upon simplification yields is, A must satisfy A I 0 21. Setting x , 0 Hence the vector and constant results in the algebraic equations ________________________________________________________________________ page 373 —————————————————————————— CHAPTER 7. —— . For a nonzero solution, we must have A I the characteristic equation are and . With reduces to . The corresponding eigenvector is case , the system is equivalent to the equation It follows that x . The roots of , the system of equations For the . An eigenvector is and x The Wronskian of this solution set is xx . Thus the solutions are linearly independent for . Hence the general solution is x 22. As shown in Prob. , solution of the ODE requ...
View Full Document

This note was uploaded on 03/11/2014 for the course MA 303 taught by Professor Staff during the Spring '08 term at Purdue University.

Ask a homework question - tutors are online