Register to reply

Inhomogeneous diff EQ, undetermined coefficients

by offbeatjumi
Tags: coefficients, diff, inhomogeneous, undetermined
Share this thread:
offbeatjumi
#1
Mar4-10, 02:25 PM
P: 29
Find the solution of:

y" + 3y' = 72sin(3t) + 36cos(3t)
where y(0) = 6 and y'(0) = 9

I first found the solution to the homogeneous eq:

the roots (R^2 + 3R = 0) are R = 0, -3
which gives the family of solutions:
y = a(1) + be^(-3t)
and y' = -3be^(-3t)

using the initial conditions (maybe Im not supposed to use them here?)
I find a = 9, b = -3

For the inhomogeneous eq:

I try (guess)
y = Asin(3t) + Bsin(3t)
y' = 3Acos(3t) - 3Bsin(3t)
y" = -9Asin(3t) - 9Bcos(3t)

substitute those values into the original equation (left hand side) I find

sin3t(-9A-9B) + cos3t(-9B-9A) = 72sin3t + 36cos3t

therefore
-9A - 9B = 72
-9B - 9A = 36
giving B = -6, A = -2


Therefore I get the solution:

y = 9 - 3e^(-3t) - 2sin3t - 6cos3t

What did I do wrong (this answer is incorrect)
Thanks
Phys.Org News Partner Science news on Phys.org
'Smart material' chin strap harvests energy from chewing
King Richard III died painfully on battlefield
Capturing ancient Maya sites from both a rat's and a 'bat's eye view'
tiny-tim
#2
Mar4-10, 03:16 PM
Sci Advisor
HW Helper
Thanks
tiny-tim's Avatar
P: 26,148
Hi offbeatjumi!
Quote Quote by offbeatjumi View Post
where y(0) = 6 and y'(0) = 9

using the initial conditions (maybe Im not supposed to use them here?)
I find a = 9, b = -3

Therefore I get the solution:

y = 9 - 3e^(-3t) - 2sin3t - 6cos3t
But y(0) ≠ 6, is it?

So you did need to wait until the end before finding the constants.
offbeatjumi
#3
Mar4-10, 08:23 PM
P: 29
thank you! i wasn't sure about where to apply initial conditions


Register to reply

Related Discussions
Help undetermined coefficients Differential Equations 4
Undetermined coefficients Differential Equations 2
Method of Undetermined Coefficients - Inhomogeneous DE Differential Equations 4
Dif Eq - Undetermined Coefficients Calculus & Beyond Homework 3
Diff Eq Undetermined Coefficients Calculus & Beyond Homework 2