Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
cke8
Group Title
Please help me solve
y''(x)+6 y'(x)+13 y(x) = 4 e^(3 x) sin(2 x), y(0) = 1, y'(0) = 2
 one year ago
 one year ago
cke8 Group Title
Please help me solve y''(x)+6 y'(x)+13 y(x) = 4 e^(3 x) sin(2 x), y(0) = 1, y'(0) = 2
 one year ago
 one year ago

This Question is Closed

SithsAndGiggles Group TitleBest ResponseYou've already chosen the best response.1
\[y''+6y'+13y=4e^{3x}\sin(2x),\; y(0)=1,\; y'(0)=2\] Homogeneous solution: \[r^2+6r+13=0\\ r=\frac{6\pm\sqrt{16}}{2}=3\pm4i\\ y_c=e^{3x}\left(C_1\cos(4x)+C_2\sin(4x)\right)\] Nonhomogeneous solution: Using the method of undetermined coefficients, try (as a guess) \[y_p=Ae^{3x}\sin(2x)+Be^{3x}\cos(2x)\] I'll leave that work to you, since it'd be a pain to type it all out, but I'll be available to check what you get later. The general solution will then be \[y=y_c+y_p\]
 one year ago

cke8 Group TitleBest ResponseYou've already chosen the best response.0
Could you please explain a bit more?
 one year ago

abb0t Group TitleBest ResponseYou've already chosen the best response.0
I think the explanation provided is quite clear.
 one year ago

SithsAndGiggles Group TitleBest ResponseYou've already chosen the best response.1
@cke8, which part? The homogeneous solution, or the clue for the nonhomogeneous one?
 one year ago

cke8 Group TitleBest ResponseYou've already chosen the best response.0
The clue for the nonhomogenous one. Thanks!
 one year ago

SithsAndGiggles Group TitleBest ResponseYou've already chosen the best response.1
\[\begin{align*}y_p&=Ae^{3x}\sin(2x)+Be^{3x}\cos(2x)\\ &=e^{3x}\left(A\sin(2x)+B\cos(2x)\right)\\\\ y_p'&=3e^{3x}\left(A\sin(2x)+B\cos(2x)\right)+e^{3x}\left(2A\cos(2x)2B\sin(2x)\right)\\ &=e^{3x}\left[(3A2B)\sin(2x)+(3B+2A)\cos(2x)\right]\\\\ y_p''&=3e^{3x}\left[(3A2B)\sin(2x)+(3B+2A)\cos(2x)\right]\\&\;\;\;\;\;+e^{3x}\left[(6A4B)\cos(2x)+(6B4A)\sin(2x)\right]\\ &=e^{3x}[(5A+12B)\sin(2x)+(5B12A)\cos(2x)] \end{align*}\] Now plug in y_p'', y_p', and y_p into the original equation and solve for A and B. It seems daunting, but doable. Be sure to keep track of your coefficients and their signs.
 one year ago
See more questions >>>
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.