Test2A_Fall06_Key

Test2A_Fall06_Key - Test 2A Fall 06 KEY 1. y 2 y 3 y = e 3...

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Test 2A Fall 06 KEY 1. x e y y y 3 3 2 = Solve the reduced equation x x e C e C y r r r r r y y y + = = = + = = 2 3 1 2 1 , 3 0 ) 1 )( 3 ( 0 3 2 0 3 2 Now solve for the particular solution x x x x x x Axe Ae Ae z Axe Ae z Axe z 3 3 3 3 3 3 9 3 3 3 + + = + = = Plug in the z’s in to your differential equation 0 0 0 3 6 9 4 / 1 1 4 1 2 3 3 3 3 = = = = = + A A A xe A A A A A e x x Plug in you’re a into z x xe z 3 4 1 = 2. 1 ) 2 cos( 4 2 4 4 2 + = + x e y y y x Solve the reduce equation {} x x xe e r r r r r y y y 2 2 2 , 2 , 2 0 ) 2 )( 2 ( 0 4 4 0 4 4 = = = + = + Find z. The D at the end can be any letter you want it to be, so don’t be confused when they put another letter in the test. Also it can have different sign but that doesn’t matter. D x C x B e Ax z x + + + = ) 2 sin( ) 2 cos( 2 2 3. 9 2 4 ) ( 2 2 + + = s s s s F Break it up into fractions
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9 2 9 4 ) ( 2 2 2 + + + = s s s s s F Now you take the laplace inverse but you cant do it for the last one because it looks like the sin(x) but it needs a 3 on top. 3 2 9 3 9 4 ) ( 3 3 9 2 9 4 ) ( 2 2 2 2 2 2 + + + = + + + = s s s s s F s s s s s F Now you can take the laplace inverse. ) 3
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Test2A_Fall06_Key - Test 2A Fall 06 KEY 1. y 2 y 3 y = e 3...

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