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Unformatted text preview: (a) v ( x ) = 1 /x 2 (b) v ( x, t ) = t ( t + x ) (c) u ( x, t ) = xe t 3. [20 points] Is there any constant f such that u ( t ) = e t is a solution of the ODE d 2 u dt 2 + 4 du dt3 u = f ? If so, specify f . Otherwise, explain why no such f exists. 4. [20 points] Suppose that you have a solution u of the equation a ( t ) d 2 u dt 2 + b ( t ) du dt + c ( t ) u ( t ) = f ( t ) (1) and that v is a nonzero solution of the homogeneous equation a ( t ) d 2 u dt 2 + b ( t ) du dt + c ( t ) u ( t ) = 0 . Explain how to produce innitely many dierent solutions of (1)....
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 Fall '09
 Tompson

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