Assignment #4 Solutions

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

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern