A community for students.
Here's the question you clicked on:
 0 viewing
RolyPoly
 2 years ago
Solve \(y^{(4)}  8y''' + 26y''  40y' + 25y =0 \)
RolyPoly
 2 years ago
Solve \(y^{(4)}  8y''' + 26y''  40y' + 25y =0 \)

This Question is Closed

RolyPoly
 2 years ago
Best ResponseYou've already chosen the best response.0\[y^{(4)}  8y''' + 26y''  40y' + 25y =0 \] \[λ^4  8λ^3 + 26λ^2 40λ + 25 =0 \] \[(λ^2 4λ + 5)^2 = 0\] λ = (2+i) (repeated) or λ = 2i (repeated) \[y = c_{1} e^{(2+i)x} + c_{2} x e^{(2+i)x} + c_{3} e^{(2i)x} + c_{4} xe^{(2i)x} \]\[= e^{2x} (c_{1} e^{ix} + c_{2} x e^{ix} + c_{3} e^{ix} + c_{4} xe^{ix})\]\[= e^{2x} [c_{1} e^{ix} + c_{3} e^{ix} + x(c_{2} e^{ix} + c_{4} e^{ix})]\]\[= e^{2x} [c_{1} (cosx + isinx) + c_{3} (cos(x)+i(sin(x)) \]\[\ \ \ \ \ \ + x(c_{2} (cosx + isinx) + c_{4} (cos(x)+i(sin(x)))]\]\[= e^{2x} [(Acosx + Bsinx) + x(Ccosx + Dsinx) \]

RolyPoly
 2 years ago
Best ResponseYou've already chosen the best response.0The last line should be \[= e^{2x} [(Acosx + Bsinx) + x(Ccosx + Dsinx)]\]

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.0so far ... seems correct!!
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.