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# m238sp06t2z - y 00 y y = 0 8 t 2 y 00-ty-8 y = 0 9 y 000 6...

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Mathematics 238 test two Tuesday, May 16, 2006 1 . State the t -interval on which a solution to the following differential equation is guaranteed to exist: (4 - t 2 ) y + 2 ty + 6 y = ln t and y (1) = 0 and y (1) = 0 2 . Circle each linearly independent set of functions: ( a ) { f ( t ) = t 2 - 4 , g ( t ) = t 3 - 4 t } ( b ) { f ( t ) = sin(2 t ) , g ( t ) = sin( - 2 t ) } ( c ) { F ( t ) = e 2 t , G ( t ) = e - 2 t } 3 . Use Euler’s formula to simplify the expression e ( - 2+ i ) t - e ( - 2 - i ) t 2 i 4 . Calculate the Wronskian of the functions y 1 ( t ) = e 2 t and y 2 ( t ) = te 2 t . 5–10 . Find the general solution for 5 .
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Unformatted text preview: . y 00 + y + y = 0 8 . t 2 y 00-ty-8 y = 0 9 . y 000 + 6 y 00 + 9 y = 0 10 . y 00 + 4 y = 16-8 e 2 x 11 . Find the format for the particular solution of the following equation. It is not necessary to determine the coeﬃcients here. y 00-y = 4 t + 3-2 sin t + 4 t 2 e 3 t-e-t + 3 e-t cos t 12 . Solve the initial value problem y 00 + 9 y = 18 + 15 cos 2 t and y (0) = 0 and y (0) = 1...
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