Assignment #4 Solutions

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

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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. 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 ) = . Correct Answers: -3*exp(-3*x) + -3*exp(-7*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 ) = . Correct Answers: (0)*exp(-6*x) + (7888.76800673516)*x*exp(-6*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 ) = . Correct Answers: 1*(x**(3))*cos(-6*ln(x)) + -5*(x**(3))*sin(-6*ln(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 ) = . Correct Answers: (0)*x**(5) + (0.00374584043879357)*(x**(5))*ln(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 ) . W ( t ) = Remark: You can find W by direct computation and use Abel’s theorem as a check. You should find that W is not zero and so y 1 and y 2

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