Method of undetermined coefficients
General · Mathematics
Study notes
Q: Solve y''-3y'+2y = e^x using undetermined coefficients. y_h = Ae^x+Be^(2x). RHS e^x: try y_p = Cxe^x (resonance - e^x in y_h!)... Actually: e^x IS in homogeneous: multiply by x: y_p = Axe^x. y_p' = Ae^x+Axe^x. y_p'' = 2Ae^x+Axe^x. Substitute: (2A+Axe^x)-3(A+Axe^x)+2Axe^x = e^x: -A = 1: A = -1. y_p = -xe^x. y = Ae^x+Be^(2x)-xe^x!