T2Solutions - MATH 3705C Test 2 Solutions February 16, 2007...

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MATH 3705C Test 2 Solutions February 16, 2007 Questions 1-5 are multiple choice. Circle the correct answer. Only the answer will be marked. [Marks] 1. The general solution of x 2 y 00 ¡ 2 xy 0 +3 y = 0 for x 6 =0is [3] (a) c 1 j x j 3 2 + c 2 j x j p 3 2 (b) c 1 j x j 3 2 + p 3 2 + c 2 j x j p 3 2 ¡ p 3 2 (c) j x j 3 2 + p 3 2 [ c 1 + c 2 ln j x j ] (d) j x j 3 2 h c 1 cos ³ p 3 2 ln j x j ´ + c 2 sin ³ p 3 2 ln j x j ´i (e) None of the these Solution: (d) 2. The general solution of x 2 y 00 ¡ 3 xy 0 +4 y = 0 for x 6 [3] (a) x 2 [ c 1 + c 2 ln j x j ]( b ) c 1 x 2 + c 2 x 2 (c) x 2 [ c 1 cos(ln j x j )+ c 2 sin(ln j x j )] (d) x 2 [ c 1 cos(2 ln j x j c 2 sin(2 ln j x j )] (e) None of the these Solution: (a) 3. The general solution of 2 x 2 y 00 ¡ xy 0 + y = 0 for x 6 [3] (a) c 1 j x j 1 2 + c 2 x (b) j x j 1 2 " c 1 cos à p 7 2 ln j x j ! + c 2 sin à p 7 2 ln j x j !# (c) x 2 [ c 1 cos(2 ln j x j c 2 sin(2 ln j x j )] (d) x 2 [ c 1 cos(ln j x j c 2 sin(ln j x j )] (e) None of the these Solution: (a) 4. The general solution of x 2 y 00 + xy 0 +(5 x 2 ¡ 9) y =0for x> 0is [2] (a) c 1 J 3 ( p 5 x c 2 J ¡ 3 ( p 5 x )( b ) c 1 J 3 ( p 5 x c
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T2Solutions - MATH 3705C Test 2 Solutions February 16, 2007...

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