examfinalW09sol

examfinalW09sol - N ame S ection/Time o f lecture-Professor...

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Name: ____________________________ __ Section/Time of lecture: ------------------------------ Professor I GSI: ------------------------------ TH 216 WINTER 2009 FINAL EXAM To get full score you need to carefully explain what you did. No calculators allowed. LAPLACE TRANSFORM TABLE IS ON THE SECOND PAGE 1

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Problem 1. I a-lOpt I Solve + 2y = si7 t, y(n) = 1. -+ c. - 2_ . IT -I 1:.2- 3
[b-lOpt[ Find a (particular) solution for y"- (5/t)y' + (5/t 2 )y = 8t 3 , given that the functions Yl ( t) = t and Y2 ( t) = t 5 solve the corresponding homogeneous differential equation. 4

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I c-lOpt I Find the general solution for y( 4 ) - 3y"- 4y = 0 -=-0 Y I (r-L-t 1) r _-:: -t-2 !i - } 2>< -2'1( ::; c.\ e.- -t cz. e.- -t c 3 (bj x.-+- ct.t x 5
Problem 2. Ja-lOptJSolvey" -4y' + 3y = 2et,y(O) = 3,y'(O) = 6. rl-- r -+ 3 0 Cr- > )(r-1) = o . -\: j c .:::; c.\ -e -+ CL .e, jp;:: A le_t ;\-te,.f:, Jf . -t jt-= ( A-le}-)-'-! (A-t-\:--t -b) -t :>AtL{"'" 2 e__-t A -:::::.-1 6

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b-lOpt I Solve the following system of ordinary differential equations x' = 5x + 4y y' = -4x +5y (s _ \ }_ -r 1 G = o S\:= 7
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examfinalW09sol - N ame S ection/Time o f lecture-Professor...

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