AnswerGuide2 - Answer Guide 2 Math 427K: Unique Number...

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Answer Guide 2 Math 427K: Unique Number 55160 Wednesday, September 7, 2011 x ( t ) of the di/erential equation. 1. dx dt + 2 x t = t 1 ( t > 0) Solution: The general solution is: x ( t ) = Ct 2 + 1 4 t 2 1 3 t: ( F ) 2. x 0 x tan t 2 sin t = 0 ( 2 < t < 2 ) Solution: The general solution is: x ( t ) = C cos(2 t ) 2 cos t : ( F ) 3. (1 + t 2 ) x 0 2 tx = 3 + 3 t 2 Solution: The general solution is: x ( t ) = ( C + 3 arctan t )(1 + t 2 ) : ( F ) 4. x 0 x t ln t + 3 t = 0 ( t > 0) Solution: The general solution is: x ( t ) = j ln t j ( C 3 j ln j ln t jj ) : ( F ) 5. dx dt = x t ( x 1) ; x (1) = 2 (An implicit solution is OK here.) Solution: The general solution in implicit form is t = C e x ( t ) x ( t ) : ( F ) The initial condition forces C = 2 e 2 .
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6. dx dt = t 3 x ; x (0) = 4 Solution: The general solution is x ( t ) = 3 ± p 9 A t 2 = 3 ± p B t 2 : ( F ) The initial condition makes us choose the negative branch and set B = 49 , yielding x ( t ) = 3 p 49 t 2 : ( FF ) 7. dx
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This note was uploaded on 10/24/2011 for the course MATH 427K taught by Professor Delallave during the Spring '11 term at University of Texas at Austin.

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AnswerGuide2 - Answer Guide 2 Math 427K: Unique Number...

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