141Bquiz9c - 1 3 (3 + 2 e ), C) 1 3 (-1 + e ), D) 2 3 (1 +...

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1 MATH 141B Quiz#9 Due: Friday March 28, 2008 [ 2 ] 1. Consider the initial value problem y ′′ + y - 12 y = 0 y (0) = 1 , y (0) = - 1 The homogeneous diferential equation has general solution has the ±orm y h = c 1 e r 1 x + c 2 e r 2 x , where r 1 and r 2 are the roots o± the auxiliary equation. Label r 1 and r 2 so that r 1 < r 2 (that is, r 1 is ±urther to the le±t on the number line). Find c 1 . A) 1 2 , B) - 2 7 , C) 3 7 , D) 4 7 , E) none o± the above [ 2 ] 2. Solve the initial value problem y ′′ - 6 y + 12 y = 3 y (0) = - 1 , y (0) = 2 ±or y ( x ) and compute y ( 1 3 ) . A) 1 3 (1 + 2 e ), B) 1 3 (2 + 3 e ), C) 1 3 ( - 1 + e ), D) 2 3 (1 + e ), E) none o± the above
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2 [ 2 ] 3. Solve the initial value problem y ′′′ + 6 y ′′ + 9 y = 0 y (0) = 2 , y (0) = - 2 y ′′ (0) = 3 for y ( x ) and compute y ( - 1 3 ) . A) 1 3 (1 + 2 e ), B)
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Unformatted text preview: 1 3 (3 + 2 e ), C) 1 3 (-1 + e ), D) 2 3 (1 + e ), E) none of the above [ 2 ] 4. For the non-homogeneous dierential equation y -y = 2 x-1 , which of the following is the correct form of a particular solution y p to start with. A) Ax , B) Ax 2 , C) Ax 2 + Bx , D) Ax 2 + Bx + C , E) none of the above [ 2 ] 5. For the non-homogeneous dierential equation y -y = 2 x 3 , which of the following is the correct form of a particular solution y p to start with. A) Ax 3 B) Ax 4 C) Ax 5 D) Ax 5 + Bx 4 + Cx 3 + Dx 2 + Ex + F E) none of the above...
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141Bquiz9c - 1 3 (3 + 2 e ), C) 1 3 (-1 + e ), D) 2 3 (1 +...

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