First-Order Equations, Separable Equations- Problem Set

First-Order Equations, Separable Equations- Problem Set -...

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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 () c o s y dy xdx y + = 1 (2 ) c o s ydy xdx y += ∫∫ 2 ln sin yy xC + =+ Using the initial value, 2 ln 1 (1) sin(0) C + 01 0 C + 1 C = 2 ln sin 1 x + 2. 34 xx dy e e dx y = + , (0) 1 y = dy e e dx y = + (3 4 ) ( ) e e dx (3 4 ) ( ) e 2 32 e e C + =− + Using the initial value, 32 11 C −−+ 7 C = 2 7 ee + 3. 2cos2 dy x dx y = + , (0) 1 y dy x dx y = + (3 2 ) (2cos 2 ) (3 2 ) (2cos 2 ) 2 3s i n 2 + Using the initial value, 31 0 C −+= + 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 + = 32 4( 1 ) ydy xx dx =+ 1 ) ydy xx 42 4 yC = ++ Using the initial value, 1 00 4 C =++ 1 4 C =
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This note was uploaded on 10/08/2010 for the course GE 207K taught by Professor None during the Fall '10 term at University of Texas at Austin.

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First-Order Equations, Separable Equations- Problem Set -...

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