complimentary function of the differential equation
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x'' + 2x' + 3x = sin (wt)
Let x_c = ce^{\lambda x}, so
\lambda^2 + 2\lambda + 3 = 0
Therefore \lambda_1 = 4i - 1, \lambda_2 = 4i + 1
Could anyone possibly tell me what the complementary function then is? My instinct is to use x_c = c_1cos (wt) + c_2sin (wt) but I'm not sure when it's imaginary numbers whether you have to sub these in somewhere?? thanks in advance!
Let x_c = ce^{\lambda x}, so
\lambda^2 + 2\lambda + 3 = 0
Therefore \lambda_1 = 4i - 1, \lambda_2 = 4i + 1
Could anyone possibly tell me what the complementary function then is? My instinct is to use x_c = c_1cos (wt) + c_2sin (wt) but I'm not sure when it's imaginary numbers whether you have to sub these in somewhere?? thanks in advance!
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