This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 solutions 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...
View Full
Document
 Spring '09
 EWQFQW

Click to edit the document details