Sample Problems for Exam Three 1. Solve the system x0 = x-4 y ; y0 = x + y 2. Factor the di±erential equation y 00-3 y0 +2 y = x into two ﬁrst order equations and solve. 3. Find the general solution of y 000-3 y0 + 2 y = 0. 4. What does it mean to say that y 1 , y 2 and y 3 are independent? Show that x , x 2-1 and x 2-4 are independent using the deﬁnition. 5. Find the general solution of y ( viii )-y ( vii )-y ( iv ) + y ( iii ) = 0, given that r 8-r 7-r 4 + r 3 = r 3 ( r-1) 2 ( r + 1)( r 2 + 1). 6. Use Undetermined Coe²cients to solve y 000-y 00 + 4 y0-4 y = cosx . 7. Find a ﬁfth order linear di±erential equation with general solution y = c 1 e 2 t + c 2 e-2 t + c 3 te-2 t + c 4 cos 2 t + c 5 sin 2 t . 8. (a) Find the general solution to the Cauchy-Euler equation L [ y ] = x 3 y 000-x 2 y 00 + 2 xy0 +-2 y = 0. (b) Find a particular solution of L [ y ] = x 3 by Undetermined Coe²cients. (c) Find the solution of
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This note was uploaded on 12/15/2011 for the course MAP 2302 taught by Professor Tuncer during the Spring '08 term at University of Florida.