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T2Solutions

# T2Solutions - MATH 1005A Test 2 Solutions[Marks[3 Questions...

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MATH 1005A Test 2 Solutions February 13, 2009 Questions 1-5 are multiple choice. Circle the correct answer. Only the answer will be marked. [Marks] 1. Two independent solutions of 2 y 00 +5 y 0 ¡ 3 y =0aregivenby [3] (a) y 1 = e x= 2 ;y 2 = e ¡ 3 x ( b ) y 1 = e ¡ 5+ p 37 2 x ;y 2 = e ¡ 5 ¡ p 37 2 x ( c ) y 1 = e ¡ 5 2 x cos Ã p 37 2 x ! ;y 2 = e ¡ 5 2 x sin Ã p 37 2 x ! ( d ) y 1 = e ¡ 3 x ;y 2 = xe ¡ 3 x (e) None of these Solution: (a) 2. The general solution of y 00 +6 y 0 +9 y =0isg ivenby [3] (a) y = c 1 e ¡ 3 x + c 2 e ¡ 3 x ( b ) y = c 1 e ¡ 3 x + c 2 xe ¡ 3 x ( c ) y = c 1 e ¡ 3 x + c 2 e ¡ 3 x ln j x j ( d ) y = c 1 e ¡ 3 x cos( x )+ c 2 e ¡ 3 x sin( x ) (e) None of these Solution: (b) 3. The general solution of y 00 ¡ 8 y 0 +25 y =0isg ivenby [3] (a) c 1 e 4 x + c 2 e 3 x ( b ) c 1 cos(3 x )+ c 2 sin(3 x )( c ) e 4 x [ c 1 cos(3 x )+ c 2 sin(3 x )] ( d ) c 1 e 3 x cos(4 x )+ c 2 e 3 x sin(4 x ) (e) None of these Solution: (c)

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T2Solutions - MATH 1005A Test 2 Solutions[Marks[3 Questions...

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