2.2 Separable Equations

# 2.2 Separable Equations - First-Order Equations Separable...

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1 First-Order Equations: Separable Equations- Problem Set 1. 2 cos 12 dy y x dx y ± , (0) 1 y 2 cos dy y x dx y ± ² 2 () c o s y dy xdx y ± ² 1 (2 ) c o s ydy xdx y ± ³³ ² 2 ln sin yy xC ± ± Using the initial value, 2 ln 1 (1) sin(0) C ± ² 010 C ± ± ² 1 C 2 ln sin 1 x ± 2. 34 xx dy e e dx y ´ ´ ± , (0) 1 y dy e e dx y ´ ´ ± ² (3 4 ) ( ) e e dx ´ ´ ² (3 4 ) ( ) e ´ ´ ³ ³ ² 2 32 e e C ´ ± ´ ´ ± Using the initial value, 32 11 C ´´± ² 7 C 2 7 ee ´ ´ ´ ± 3. 2cos2 dy x dx y ± , (0) 1 y ´ dy x dx y ± ² (3 2 ) (2cos 2 ) ² (3 2 ) (2cos 2 ) ³ ³ ² 2 3s i n 2 ± ± Using the initial value, 31 0 C ´± ± ² 2 C ´ 2 i n 2 2 x ´ 4. 2 3 (1 ) 4 dy x x dx y ± , 1 (0) 2 y ´

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2 2 3 (1 ) 4 dy x x dx y ± ² 32 4( 1 ) ydy xx dx ± ² 1 ) ydy xx ± ³ ³ ² 42 4 yC ±± Using the initial value, 1 00 4 C ² 1 4 C ² 4 1 4 y
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## This note was uploaded on 02/03/2012 for the course M 427K taught by Professor Fonken during the Fall '08 term at University of Texas.

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2.2 Separable Equations - First-Order Equations Separable...

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