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Unformatted text preview: Mathematics 238 first test Monday, July 7, 2008 1 . Is y = e 4 x a solution to the differential equation y 00 5 y + 4 y = 0 ? Substitute the proposed solution into the differential equation: 16 e 4 x 5 4 e 4 x + 4 e 4 x = 0 So y = e 4 x is a solution to the differential equation 2 . Is y = Z x cos t 2 dt a solution of the initial value problem dy dx = cos x 2 and y (0) = 0 ? yes 3 . Given the differential equation dy dx = ( x 2 sec 3 x ) y ( a ) Is the equation separable? yes ( b ) Is the equation linear? yes ( c ) Is the equation exact? yes 4 . Given the differential equation 3 x 2 y 2 + 2 x 3 y + 12 y 2 dy dx = 0 ( a ) Is the equation separable? no ( b ) Is the equation linear? no ( c ) Is the equation exact? yes ∂ ∂y (3 x 2 y 2 ) = ∂ ∂x (2 x 3 y + 12 y 2 ) 5 . Solve the initial value problem dy dx = y 3 (2 x 5) and y (0) = √ 3 6 and state the solution’s domain. Z dy y 3 = Z (2 x 5) dx = ⇒ y = 1 √ 2 x 2 + 10 x + 12 = 1 q 2( x + 1)( x 6) domain: 1 ≤ x ≤ 6 6...
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 Spring '09
 EWQFQW
 Exponential Function, Boundary value problem, dx, dy

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