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Math 2233 Homework Set 3 1. Determine the order of the following diﬀerential equations and whether or not the equations are linear. (a) x 2 d 2 y dx 2 + x dy dx +2 y = sin( x ) (b) (1 + y 2 ) d 2 y dx 2 + x dy dx + y = e x (c) d 4 y dx 4 + d 3 y dx 3 + d 2 y dx 2 + dy dx + y =1 (d) dy dx + xy 2 =0 (e) d 2 y dx 2 + sin( x + y ) = sin( x ) 2. Solve y +3 y = x + e - 2 x . 3. Solve y - y =2 e x . 4. Solve xy y = sin( x ); x> 0 . 5. Solve the following initial value problem. y - y xe 2 x ; y (1) = 0 . 6. Solve the following initial value problem. y + 2 x y = cos( x ) x 2 ; y ( π )=0 7. Find the solution of the initial value problem below. State the interval in which the solution is valid. xy y = x 2 - x +1 ; y (1) = 1 2 . 8. Find the solution of the initial value problem below. State the interval in which the solution is valid.
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This homework help was uploaded on 04/22/2008 for the course MATH 2233 taught by Professor Binegar during the Spring '08 term at Oklahoma State.

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