L02 - Review Differential equations, Classification, Com-...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

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

Unformatted text preview: Review Differential equations, Classification, Com- plete Solution (Reduction to Integration) of FOLODE. Example: The FOLODE is y + 3 t y = t n . Review Differential equations, Classification, Com- plete Solution (Reduction to Integration) of FOLODE. Example: The FOLODE is y + 3 t y = t n . We multiply by the integrating factor e integraltext 3 /t dt = e 3 ln t = t 3 and get t 3 ( y + 3 t y ) bracehtipupleft bracehtipdownrightbracehtipdownleft bracehtipupright = ( t 3 y ) = t n +3 , whence t 3 y ( t ) = t n +4 n + 4 + C and y ( t ) = t n +1 n + 4 + C t 3 . Well consider general FOODEs y ( t ) = f ( t, y ( t ) ) , y ( t ) = dy ( t ) dt , for a while. The function f of two vari- ables t, y is called the coupling coefficient , vis. dy ( t ) = f ( t, y ( t ) ) dt 2 Direction Fields The slope is f ( t, y ) ( t, y ) t y A Direction Field 3 ( t, y ) t y The blue curves y = y ( t ) satisfiy y ( t ) = f ( t, y ( t )) The slope is f ( t, y ). at every point ( t, y ) of the t, y plane. A Direction Field plus two solutions 4 Existence and Uniqueness Theorem: Suppose the function f ( t, y ) and its partial derivatives...
View Full Document

Page1 / 16

L02 - Review Differential equations, Classification, Com-...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online