Answers>Further Mathematics>A Level>Article

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

Answered by Edward O. • Further Mathematics tutor

4423 Views

Find the general solution to: d^(2)x/dt^(2) + 7 dx/dt + 12x = 2e^(-t)

Related Further Mathematics A Level answers

Find the integral of f(x)= x^3 + 2x^2 + 1

Prove by induction that (n^3)-n is divisible by 3 for all integers n>0 (typical fp1 problem)

Find all square roots of the number 3 + 4i.

How do I find and plot the roots of a polynomial with complex roots on an Argand diagram? e.g. f(z) =z^3 -3z^2 + z + 5 where one of the roots is known to be 2+i