inhomogeneous diff EQ, undetermined coefficientsby offbeatjumi Tags: coefficients, diff, inhomogeneous, undetermined 

#1
Mar410, 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(9A9B) + cos3t(9B9A) = 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 



#2
Mar410, 03:16 PM

Sci Advisor
HW Helper
Thanks
P: 26,167

Hi offbeatjumi!
So you did need to wait until the end before finding the constants. 



#3
Mar410, 08:23 PM

P: 29

thank you! i wasn't sure about where to apply initial conditions



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