# Y y 0 a reduction of order with this solution

This preview shows page 4. Sign up to view the full content.

(*) y y 0. (a) Reduction of order with this solution involves making the substitution y ve x into equation (*) and then letting w = v . Do this substitution and obtain the constant coefficient equation that w must satisfy. (b) Obtain a the general solution to the ODE that w satisfies and then stop. (c) Explain very briefly why v can be obtained from w without actually integrating. Do not attempt to actually find v. _________________________________________________________________ Silly 10 Point Bonus: Let f ( x ) = x and g ( x ) = sin( x ). (a) It is trivial to obtain a 4th order homogeneous linear constant coefficient ordinary differential equation with f and g as solutions. Do so. (b) It’s only slightly messier to obtain a 2nd order homogeneous linear ordinary differential equation with { f , g } as a fundamental set of solutions. Do so. [Say where your work is, for it won’t fit here.]
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• 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.

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

• 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.

Dana University of Pennsylvania ‘17, Course Hero Intern

• 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.

Jill Tulane University ‘16, Course Hero Intern