3354_f05_st2

3354_f05_st2 - y 00-3 y + 2 y = 2 te t + 8 sin(2 t )....

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Math 3354, Sample Test # 2, Name 1. Use a substitution y = x 0 to solve the problem xx 00 = ( x 0 ) 2 ANSWER: x = c 2 e c 1 t 2. Solve the initial value problem y 00 + y 0 - 2 y = 0 y (0) = 4, y 0 (0) = 1. ANSWER: y = 3 e t + e - 2 t 3. Solve the initial value problem y 00 - 2 y 0 + 10 y = 0 y (0) = 4, y 0 (0) = 1. ANSWER: y = e t (4 cos(3 t ) - sin(3 t )) 4. Find the general solution of x 2 y 00 + 3 xy 0 + y = 0 ( Answer must be in x ). ANSWER: y = c 1 x - 1 + c 2 ln( x ) x - 1 5. Find the general solution of y ( iv ) - 13 y 00 + 36 y = 0. ANSWER: y = c 1 e 2 t + c 2 e - 2 t + c 3 e 3 t + c 4 e - 3 t 6. Find the form of a particular solution y p ( t ) for (DO NOT SOLVE FOR CONSTANTS)
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Unformatted text preview: y 00-3 y + 2 y = 2 te t + 8 sin(2 t ). ANSWER: y = t ( A 1 t + A 2 ) e t + A 3 sin(2 t ) + A 4 cos(2 t ) 7. Use undetermined coeﬃcients to ﬁnd a particular solution for y 00-3 y + 2 y = 10 sin( t ). ANSWER: y p = 3 cos( t ) + sin( t ) 8. Use variation of parameters to ﬁnd a particular solution for y 00-2 y + y = 35 e t t 3 / 2 . ANSWER: y = 4 t 7 / 2 e t...
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This note was uploaded on 10/19/2011 for the course MATH 2254 taught by Professor Gilliam during the Fall '05 term at Texas Tech.

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