Assignment #4 - Stephanie Campbell due at 11:55pm EDT...

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Stephanie Campbell Assignment 4 MATH263, Fall 2010 due 10/16/2010 at 11:55pm EDT. You may attempt any problem an unlimited number of times. 1. (1 pt) Find a fundamental set of solutions { y 1 ( x ) , y 2 ( x ) } of the equation d 2 y dx 2 - 18 dy dx + 81 y = 0 . y 1 ( x ) = . y 2 ( x ) = . 2. (1 pt) Solve the initial value problem d 2 y dx 2 + 10 dy dx + 21 y = 0 , y ( 0 ) = - 6 , y ( 0 ) = 30 y ( x ) = . 3. (1 pt) Solve the boundary value problem d 2 y dx 2 + 12 dy dx + 36 y = 0 , y ( 0 ) = 0 , y ( π / 2 ) = 1 y ( x ) = . 4. (1 pt) Find a fundamental set of solutions { y 1 ( x ) , y 2 ( x ) } of the equation x 2 d 2 y dx 2 - 11 x dy dx + 61 y = 0 . in the interval x > 0. y 1 ( x ) = . y 2 ( x ) = . 5. (1 pt) Solve the initial value problem x 2 d 2 y dx 2 - 5 x dy dx + 45 y = 0 , y ( 1 ) = 1 , y ( 1 ) = 33 y ( x ) = . 6. (1 pt) Solve the boundary value problem x 2 d 2 y dx 2 - 9 x dy dx + 25 y = 0 , y ( 1 ) = 0 , y ( 3 ) = 1 y ( x ) = . 7. (1 pt) Find the function y 1 of t which is the solution of 81 y + 36 y - 5 y = 0 with initial conditions y 1 ( 0 ) = 1 , y 1 ( 0 ) = 0 . y 1 = Find the function y 2 of t which is the solution of 81 y + 36 y - 5 y = 0 with initial conditions y 2 ( 0 ) = 0 , y 2 ( 0 ) = 1 . y 2 = Find the Wronskian W ( t ) = W ( y 1 , y 2 ) .
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