# quiz - + y = sin 2 ( t ) describes undamped oscillations...

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MATH 2930: Quiz 1 October 29, 2009 Problem 1. For each of the following statements, indicate whether it’s True or False and explain your reasoning. (a) The functions f ( x ) = e x , g ( x ) = cos x , h ( x ) = sin x are linearly independent on the real line. (b) If the function y 1 ( x ) = x sin x is a solution of some linear homoge- neous equation with constant coeﬃcients, then the function y 2 ( x ) = sin x is also a solution of the same equation. 1

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(c) 3 sin(5 t ) - 4 cos(5 t ) = 5 cos(5 t - α ) , where α = - arctan(3 / 4) . Problem 2. Find a linear homogeneous constant-coeﬃcient equation with the general solution y = A cos(2 x + B ) + Cx sin(2 x + D ) . Problem 3. The equation y 00

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Unformatted text preview: + y = sin 2 ( t ) describes undamped oscillations under the inuence of the external force F ( t ) = sin 2 ( t ) . Find all values of such that this equation has unbounded solutions. 2 Problem 4. y c = c 1 x 2 + c 2 x 3 is a complementary function of the equation x 2 y 00-4 xy + 6 y = x 3 . Find a particular solution of this equation on the interval x &gt; . Problem 5. Find a general solution of the equation x 2 y 00-3 xy + 4 y = 0 on the interval x &gt; . (Hint: make the substitution v = ln x .) 3 Blank page 4...
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## This note was uploaded on 11/17/2009 for the course MATH 2930 at Cornell University (Engineering School).

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quiz - + y = sin 2 ( t ) describes undamped oscillations...

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