Lesson 4a - Homogeneous

C e lnu 1 eu ax u 1 e ax y 1 x y x y e ax 1 x

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Unformatted text preview: ln| x| c eu e ln| x|e c e ln|u 1| eu Ax u 1 e Ax y 1 x y x y e Ax( 1) x Example 3 xy y x2 y2 x y y x y' y 1 ( )2 x x Determine the general solution to the following ODE: y ' xy xy x2 x2 y2 x2 y2 x2 y xy x x y 1 ( y )2 x y Thus y ' xu 'u Let u , x 2 u u 2 1 u u xu ' 1 u2 xu 'u 1 u 1 u' u x 2 1u 1 ( )u ' uu x 1 1 ( u )u ' u x 1 du 1 ( u u ) dx dx x dx 1 1 ( u )du dx u x u2 ln | u | ln | x | c 2 2 ln | u | u 2 2 ln | x | c y y2 2 ln | | 2 ln | x | ( ) c x x y y2 2 ln | 2 | ( ) c x x...
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This note was uploaded on 02/07/2014 for the course MATH 1004 taught by Professor Mark during the Summer '00 term at Carleton CA.

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