HW 1 solution - EGM 4313 S08 Homework Solution #1 EGM 4313...

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EGM 4313 S08 Homework Solution #1 1/11 EGM 4313 S08 - Homework#1 1. Problem Set 1.3, pp 18, #4 Find a general solution. Show the steps of derivation. Check your answer by substitution. 2 ) 9 ( ' x y y + = ,( v x y = + 9 ) e q 1 Solution: Step 1: Let v x y = + 9 Æ x v y 9 = ( 1 ) e q 2 Differentiate eq 2 9 ' ' = v y e q 3 Sub. eq 2 and 3 into eq 1 2 9 ' v v = Æ 9 2 + = v dx dv Æ dx v dv = + 9 2 Step 2: Integrate both sides c x v + = 3 ) 3 arctan( ,where ) arctan( 1 2 2 a v a dv a v dv = + eq 4 Sub eq 2 into eq 4 c x x y + = + 3 ) 3 9 arctan( Check the answer by substation: ) 3 tan( 3 9 c x x y + = + Æ x c x y 9 ) 3 tan( 3 + = e q 5 Differentiate eq 5 9 ) 3 ( sec 9 ' 2 + = c x y ,where x dx x d 2 sec ) (tan = e q 6 Sub eq 5 and 6 into eq 1 2 2 2 2 ) 9 ( ) 3 ( tan 9 ) 1 ) 3 ( (sec 9 9 ) 3 ( sec 9 ' x y c x c x c x y + = + = + = + =
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EGM 4313 S08 Homework Solution #1 2/11 2. Problem Set 1.3, pp 18, #17 Find the particular solution. Show the steps of derivation, beginning with the general solution. y x x y = ln ' , 8 1 ln ) 3 ( = y e q 1 Solution: Step 1: y x x dx dy = ln Æ x x dx y dy ln = e q 2 Integrate eq 2 ' ) ln(ln ln c x y + = e q 3 Take exponents on both sides x c e e e y x c c x ln ) ln(ln ' ) ' ) (ln(ln = = = + e q 4 Step 2: Apply the initial condition c c 3 ln 3 ln 3 ln 81 ln 4 = = = Æ c=4 x y ln 4 =
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EGM 4313 S08 Homework Solution #1 3/11 3. Problem Set 1.4, p.25, #15 Test for exactness. If exact, solve. If not, use an integrating actor as given or find it by inspection or from the theorems in the text. Also, if an initial condition is given, determine the corresponding particular solution.
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This note was uploaded on 04/01/2008 for the course EGM 4313 taught by Professor Mei during the Spring '08 term at University of Florida.

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HW 1 solution - EGM 4313 S08 Homework Solution #1 EGM 4313...

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