{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

285lect14 - 1 Lecture 14 We observe from the previous...

This preview shows pages 1–2. Sign up to view the full content.

1 Lecture 14 We observe from the previous example how one can try to solve the initial value problem y 00 + p ( x ) y 0 + q ( x ) y = 0; y ( x 0 ) = y 0 ; y 0 ( x 0 ) = y 0 0 : ° We need to know that the particular solution satisfying given initial value problem is unique. ° We should °nd two particular solutions y 1 ( x ) ; y 2 ( x ) satisfying the ODE y 00 + p ( x ) y 0 + q ( x ) y = 0 : At this point, we pay no attention to initial conditions. ° By principle of superposition, y ( x ) = C 1 y 1 ( x ) + C 2 y 2 ( x ) is a solution. Now we try to select constants C 1 and C 2 in such a way that the initial conditions hold for y ( x ) . So, there are two important questions: ° Is solution of the initial value problem unique? ° What should we require from y 1 and y 2 to ensure that C 1 and C 2 can be always selected so that the solution y ( x ) = C 1 y 1 ( x )+ C 2 y 2 ( x ) satis°es the initial condition? Below, we will discuss the answers to these two fundamental questions. 1.1 Existence and uniqueness theorem for linear sec- ond order ODE We give the following theorem without proof:

This preview has intentionally blurred sections. Sign up to view the full version.

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

{[ snackBarMessage ]}

Page1 / 4

285lect14 - 1 Lecture 14 We observe from the previous...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online