Find the general solution to: d^(2)x/dt^(2) + 7 dx/dt + 12x = 2e^(-t)
"General Solution = Complimentary Function + Particular Integral"AE: m2 + 7m + 12 = 0 solve for m(m+3)=0m = -4 or -3Hence the Complimentary Function = Ae-4t + Be-3t
PI: [substitute u=ke-t]u'=-ke-tu''=ke-t[Comparing coefficients we get:]k-7k+12k=2Hence, k = 1/3.PI = 1/3 * e-tSo the general solution is:x=Ae-4t + Be-3t+ 1/3 * e-t
EO
Answered by Edward O. • Further Mathematics tutor
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