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Unformatted text preview: 18.034 Midterm #1, Sample TF Questions The exam is Wed. 03/07/07, 1:001:55pm, 1. Every solution y = y ( x ) of the DE y + 2 y = e 2 x tends to zero as x . 2. The solution of the initial value problem y y = 1 + 3 sin x, y (0) = remains bounded as x . 3. Every solution of the DE y = y 3 y is increasing in the strip 1 < y < . 2 4. The DE y = y has a constant solution. 1 + x 2 x 2 + xy + y 2 5. If y = f ( x ) is a solution of the DE y = x 2 , then so is y = (1 /k ) f ( kx ) , where k is a nonzero constant. 6. The solution to the initial value problem y = y x , y (1) = y + x is defined on x (0 , ) . 7. If p ( x ) and q ( x ) are continuous realvalued functions on the interval [ x 1 ,x 2 ] , then the initial value prob lem y + p ( x ) y = q ( x ) , y ( x 1 ) = 0 has at most one solution. 8. If two functions u 1 and u 2 are linearly independent solutions of u + p ( x ) u + q ( x ) u = 0 , where p ( x ) and q ( x ) are continuous then u 3 = u 1 + u...
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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
 HUR

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