A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 5 years ago
y''+5y'+6y=2e^t
anonymous
 5 years ago
y''+5y'+6y=2e^t

This Question is Closed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[yh(t) = \alpha e ^{2t}+\beta e ^{3t}\] \[yp(t) = 1/20e ^{2t}\] Therefore \[Y(t) = \alpha e ^{2t} + \beta e ^{3t} + 1/20e ^{2t}\] Look right?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0does it look righht? yes.... can i prove its right...fraid not :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0That's cool. Thanks for taking a look.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0It does not look right to me.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The solution of the associated homogeneous equation: \[y''+5y'+6y=0\] can be found using the auxiliary equation: \[m^2+5m+6=0 \implies (m+3)(m+2)=0 \implies m=3, m=2\] Hence the complementary solution is: \[y_c=c_1e^{2t}+c_2e^{3t}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Let's assume a solution of the form Ae^x for the particular solution, then substituting in the original function gives: \[Ae^t+5Ae^t+6Ae^t=2e^t \implies 12A=2 \implies A={1 \over 6}\] Therefore, the particular solution is y_p=e^t/6 That's the general solution of the differential equation is: \[y=y_c+y_p=c_1e^{2t}+c_2e^{3t}+{e^t \over 6}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ok. Thank you. I think I combined two questions into one in my work, and I always misplace those pesky +/ signs. But, my logic seems correct...just my arithmetic & algebra I get lazy and sloppy with. Thank you very much.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I can tell that by looking at your answer. You're welcome.
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.