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 ) eq 1 Solution: Step 1: Let v x y = + 9 Æ x v y 9 = (1) eq 2 Differentiate eq 2 9 ' ' = v y eq 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 + = eq 5 Differentiate eq 5 9 ) 3 ( sec 9 ' 2 + = c x y ,where x dx x d 2 sec ) (tan = eq 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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