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Unformatted text preview: 18.034 Midterm #2 Name: Part I: TF Questions. Answer for each of the following statements if it is true or fale. Simply say T (if you believe it is true) or F (if you suspect it is false); you dont need to justify your answers. Each question counts 5pts. 1. Let the differential operator L [ y ] = y ( n ) + a 1 y ( n 1) + + a n y where a 1 ,...,a n are real numbers, have the characteristic polynomial p ( ) = n + a 1 n 1 + a n . If p ( ) = 0 then L [ y ] = e x has a solution of the form Ae x . 2. The solution of the initial value problem y + y 2 y = ( t ) with y (0) = y (0) = y (0) = decays exponentially as t . Here, ( t ) denotes the Dirac delta function (or the unit impulse function). 3. The curves defined parametrically as solutions of the system dx y dy 1 dt = x 2 , dt = x are orthogonal to the surface y/x = constant. 4. The function f ( x ) = x log x < x 1 , x = satisfies a Lipschitz condition....
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This note was uploaded on 07/28/2008 for the course MATH 18.034 taught by Professor Hur during the Spring '07 term at MIT.
- Spring '07