Higher-order linear ODEs with constant coefficients
General · Mathematics
Study notes
Q: Solve y''-3y'+2y = 0, y(0) = 1, y'(0) = 0. Characteristic: r²-3r+2 = (r-1)(r-2): r = 1, 2. y = Ae^x+Be^(2x). y(0) = A+B = 1. y'(0) = A+2B = 0. Solve: B = -1, A = 2. y = 2e^x-e^(2x)! Check: y(0) = 1 ✓, y'(0) = 0 ✓!