y'' - y = 0 look on the characteristic equation r² - a million = 0 r = ±a million So a typical answer to the homogeneous equation is (enable y = y(x)) y = Ae? + Be?? y(0) = A + B = 0 y(a million) = Ae + Be?¹ = a million because of the undeniable fact that A = -B, we've A = e/(e² -a million), B = e/(a million - e²) So a definite answer is y = e???¹?/(e² -a million) + e?¹???/(a million - e²) Yin
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D0: 124, 41, 8, 1, -4 , -31, -104, -247
D1: -83 -33 -7 -5 -27 -73 -143
D2: 50 26 2 -22 -46 -70
D3: -24 -24 -24 -24
D4: 0 0 0
So y(x) is a cubic function of x, and the degree is 3.
y'' - y = 0 look on the characteristic equation r² - a million = 0 r = ±a million So a typical answer to the homogeneous equation is (enable y = y(x)) y = Ae? + Be?? y(0) = A + B = 0 y(a million) = Ae + Be?¹ = a million because of the undeniable fact that A = -B, we've A = e/(e² -a million), B = e/(a million - e²) So a definite answer is y = e???¹?/(e² -a million) + e?¹???/(a million - e²) Yin