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